title: Network traffic behaviour near phase transition point

abstract:
  We explore packet traffic dynamics in a data network model near phase
transition point from free flow to congestion. The model of data network is an
abstraction of the Network Layer of the OSI (Open Systems Interconnection)
Reference Model of packet switching networks. The Network Layer is responsible
for routing packets across the network from their sources to their destinations
and for control of congestion in data networks. Using the model we investigate
spatio-temporal packets traffic dynamics near the phase transition point for
various network connection topologies, and static and adaptive routing
algorithms. We present selected simulation results and analyze them.


title: A theory for one dimensional asynchronous chemical wave

abstract:
  We present a theory for experimentally observed phenomenon of one dimensional
asynchronous waves. The general principle of coexistence of linear and
nonlinear solutions of a dynamical system is underlying the present theoretical
work. The result has been proposed analytically and numerical simulations are
produced in support of the analytical results.


title: Negative-coupling resonances in pump-coupled lasers

abstract:
  We consider coupled lasers, where the intensity deviations from the steady
state, modulate the pump of the other lasers. Most of our results are for two
lasers where the coupling constants are of opposite sign. This leads to a Hopf
bifurcation to periodic output for weak coupling. As the magnitude of the
coupling constants is increased (negatively) we observe novel amplitude effects
such as a weak coupling resonance peak and, strong coupling subharmonic
resonances and chaos. In the weak coupling regime the output is predicted by a
set of slow evolution amplitude equations. Pulsating solutions in the strong
coupling limit are described by discrete map derived from the original model.


title: Strange Nonchaotic Attractors in Harper Maps

abstract:
  We study the existence of Strange Nonchaotic Attractors (SNA) in the family
of Harper maps, proving that they are typical but not robust in this family.
Our approach is based on the theory of linear skewproducts and the spectral
theory of Schrodinger operators.


title: Radial disk heating by more than one spiral density wave

abstract:
  We consider a differentially rotating, 2D stellar disk perturbed by two
steady state spiral density waves moving at different patterns speeds. Our
investigation is based on direct numerical integration of initially circular
test-particle orbits. We examine a range of spiral strengths and spiral speeds
and show that stars in this time dependent gravitational field can be heated
(their random motions increased). This is particularly noticeable in the
simultaneous propagation of a 2-armed spiral density wave near the corotation
resonance (CR), and a weak 4-armed one near the inner and outer 4:1 Lindblad
resonances. In simulations with 2 spiral waves moving at different pattern
speeds we find: (1) the variance of the radial velocity, sigma_R^2, exceeds the
sum of the variances measured from simulations with each individual pattern;
(2) sigma_R^2 can grow with time throughout the entire simulation; (3)
sigma_R^2 is increased over a wider range of radii compared to that seen with
one spiral pattern; (4) particles diffuse radially in real space whereas they
don't when only one spiral density wave is present. Near the CR with the
stronger, 2-armed pattern, test particles are observed to migrate radially.
These effects take place at or near resonances of both spirals so we interpret
them as the result of stochastic motions. This provides a possible new
mechanism for increasing the stellar velocity dispersion in galactic disks. If
multiple spiral patterns are present in the Galaxy we predict that there should
be large variations in the stellar velocity dispersion as a function of radius.


title: Topological Mixing with Ghost Rods

abstract:
  Topological chaos relies on the periodic motion of obstacles in a
two-dimensional flow in order to form nontrivial braids. This motion generates
exponential stretching of material lines, and hence efficient mixing. Boyland
et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277
(2000)] have studied a specific periodic motion of rods that exhibits
topological chaos in a viscous fluid. We show that it is possible to extend
their work to cases where the motion of the stirring rods is topologically
trivial by considering the dynamics of special periodic points that we call
ghost rods, because they play a similar role to stirring rods. The ghost rods
framework provides a new technique for quantifying chaos and gives insight into
the mechanisms that produce chaos and mixing. Numerical simulations for Stokes
flow support our results.


title: The Size of Ghost Rods

abstract:
  'Ghost Rods' are periodic structures in a two-dimensional flow that have an
effect on material lines that is similar to real stirring rods. An example is a
periodic island: material lines exterior to it must wrap around such an island,
because determinism forbids them from crossing through it. Hence, islands act
as topological obstacles to material lines, just like physical rods, and lower
bounds on the rate of stretching of material lines can be deduced from the
motion of islands and rods. Here, we show that unstable periodic orbits can
also act as ghost rods, as long as material lines can 'fold' around the orbit,
which requires the orbit to be parabolic. We investigate the factors that
determine the effective size of ghost rods, that is, the magnitude of their
impact on material lines.


title: Nonlinear multivariate analysis of Neurophysiological Signals

abstract:
  Multivariate time series analysis is extensively used in neurophysiology with
the aim of studying the relationship between simultaneously recorded signals.
Recently, advances on information theory and nonlinear dynamical systems theory
have allowed the study of various types of synchronization from time series. In
this work, we first describe the multivariate linear methods most commonly used
in neurophysiology and show that they can be extended to assess the existence
of nonlinear interdependences between signals. We then review the concepts of
entropy and mutual information followed by a detailed description of nonlinear
methods based on the concepts of phase synchronization, generalized
synchronization and event synchronization. In all cases, we show how to apply
these methods to study different kinds of neurophysiological data. Finally, we
illustrate the use of multivariate surrogate data test for the assessment of
the strength (strong or weak) and the type (linear or nonlinear) of
interdependence between neurophysiological signals.

categories: nlin.CD physics.bio-ph physics.data-an q-bio.NC q-bio.QM


title:
Opinion formation and phase transitions in a probabilistic cellular
  automaton with two absorbing states

abstract:
  We discuss the process of opinion formation in a completely homogeneous,
democratic population using a class of probabilistic cellular automata models
with two absorbing states. Each individual can have one of two opinions that
can change according to that of his neighbors. It is dominated by an
overwhelming majority and can disagree against a marginal one. We present the
phase diagram in the mean field approximation and from numerical experiments
for the simplest nontrivial case. For arbitrarily large neighborhoods we
discuss the mean field results for a non-conformist society, where each
individual adheres to the overwhelming majority of its neighbors and choses an
opposite opinion in other cases. Mean field results and preliminary lattice
simulations with long-range connections among individuals show the presence of
coherent temporal oscillations of the population.


title: Chaos in a simple cellular automata model of a uniform society

abstract:
  In this work we study the collective behaviors arising in a model of a
simplified homogeneous society. Each agent is modeled as a binary
``perceptron'', receiving neighbors' opinions as inputs and outputting one of
two possible opinions, according to the conformist attitude and to the external
pressure of mass media. For a neighborhood size greater than three, the system
shows a very complex phase diagram, including a disordered phase and chaotic
behavior. We present analytic calculations, mean fields approximation and
numeric simulations for different values of the parameters.


title:
Discrete soliton mobility in two-dimensional waveguide arrays with
  saturable nonlinearity

abstract:
  We address the issue of mobility of localized modes in two-dimensional
nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes
e.g. discrete spatial solitons in a tight-binding approximation of
two-dimensional optical waveguide arrays made from photorefractive crystals. We
discuss numerically obtained exact stationary solutions and their stability,
focussing on three different solution families with peaks at one, two, and four
neighboring sites, respectively. When varying the power, there is a repeated
exchange of stability between these three solutions, with symmetry-broken
families of connecting intermediate stationary solutions appearing at the
bifurcation points. When the nonlinearity parameter is not too large, we
observe good mobility, and a well defined Peierls-Nabarro barrier measuring the
minimum energy necessary for rendering a stable stationary solution mobile.


title:
Colored $1/f^{\alpha}$ noise and the Order to Chaos Transition in
  Quantum Mechanics

abstract:
  The spectral statistic $\delta_n$ measures the fluctuations of the number of
energy levels around its mean value. It has been shown that chaotic quantum
systems display $1/f$ noise (pink noise) in the power spectrum $S(f)$ of the
$\delta_n$ statistic, whereas integrable ones exibit $1/f^2$ noise (brown
noise). These results have been explained on the basis of the random matrix
theory and periodic orbit theory. Recently we have analyzed the order to chaos
transition in terms of the power spectrum $S(f)$ by using the Robnik billiard
(Phys. Rev. Lett. {\bf 94}, 084101 (2005)). We have numerically found a net
power law $1/f^{\alpha}$, with $1\leq \alpha \leq 2$, at all the transition
stages. Similar results have been obtained by Santhanam and Bandyopadhyay
(Phys. Rev. Lett. {\bf 95}, 114101 (2005)) analyzing two coupled quartic
oscillators and a quantum kicked top. All these numerical results suggest that
the exponent $\alpha$ is related to the chaotic component of the classical
phase space of the quantum billiard, but a satisfactory theoretical explanation
is still lacking.


title:
Level density of the H\'enon-Heiles system above the critical barrier
  Energy

abstract:
  We discuss the coarse-grained level density of the H\'enon-Heiles system
above the barrier energy, where the system is nearly chaotic. We use periodic
orbit theory to approximate its oscillating part semiclassically via
Gutzwiller's semiclassical trace formula (extended by uniform approximations
for the contributions of bifurcating orbits). Including only a few stable and
unstable orbits, we reproduce the quantum-mechanical density of states very
accurately. We also present a perturbative calculation of the stabilities of
two infinite series of orbits (R$_n$ and L$_m$), emanating from the shortest
librating straight-line orbit (A) in a bifurcation cascade just below the
barrier, which at the barrier have two common asymptotic Lyapunov exponents
$\chi_{\rm R}$ and $\chi_{\rm L}$.


title: Drag Reduction by Bubble Oscillations

abstract:
  Drag reduction in stationary turbulent flows by bubbles is sensitive to the
dynamics of bubble oscillations. Without this dynamical effect the bubbles only
renormalize the fluid density and viscosity, an effect that by itself can only
lead to a small percentage of drag reduction. We show in this paper that the
dynamics of bubbles and their effect on the compressibility of the mixture can
lead to a much higher drag reduction.


title:
A System of n=3 Coupled Oscillators with Magnetic Terms: Symmetries and
  Integrals of Motion

abstract:
  The properties of a system of n = 3 coupled oscillators with linear terms in
the velocities (magnetic terms) depending in two parameters are studied. We
proved the existence of a bi-Hamiltonian structure arising from a
non-symplectic symmetry, as well the existence of master symmetries and
additional integrals of motion (weak superintegrability) for certain particular
values of the parameters.


title: Power solution expansions of the analogue tothe first Painleve equation

abstract:
  The fourth-order analog to the first Painlev\'{e} equation is studied. All
power expansions for solutions of this equation near points $z=0$ and
$z=\infty$ are found. The exponential additions to the expansion of solution
near $z=\infty$ are computed. The obtained results confirm the hypothesis that
the fourth-order analog of the first Painlev\'{e} equation determines new
transcendental functions. By means of the methods of power geometry the basis
of the plane lattice is also calculated.


title: Multi Solitons of a Bose-Einstein Condensate in a Three-Dimensional Ring

abstract:
  A Bose-Einstein Condensate (BEC) made of alkali-metal atoms at ultra-low
temperatures is well described by the three-dimensional cubic nonlinear
Schr\"odinger equation, the so-called Gross-Pitaevskii equation (GPE). Here we
consider an attractive BEC in a ring and by solving the GPE we predict the
existence of bright solitons with single and multi-peaks, showing that they
have a limited domain of dynamical stability. We also discuss
finite-temperature effects on the transition from the uniform phase to the
localized phase.


title: Chaotic Observer-based Synchronization Under Information Constraints

abstract:
  Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.


title: The spectral form factor for quantum graphs

abstract:
  We consider quantum graphs with spin-orbit couplings at the vertices.
Time-reversal invariance implies that the bond S-matrix is in the orthogonal or
symplectic symmetry class, depending on spin quantum number s being integer or
half-integer, respectively. The periodic-orbit expansion of the spectral form
factor is shown to acquire additional weights from spin rotations along orbits.
We determine the spin contribution to the coefficients in an expansion of the
form factor from properties of the representation of the group of spin
transformations on the graph. Consistency with the Circular Orthogonal and
Circular Symplectic Ensemble, respectively, of random matrices is obtained.


title: A geometric study of the dispersionless Boussinesq type equation

abstract:
  We discuss the dispersionless Boussinesq type equation, which is equivalent
to the Benney-Lax equation, being a system of equations of hydrodynamical type.
This equation was discussed in
<http://dx.doi.org/doi:10.1088/0305-4470/27/1/013>. The results include: a
description of local and nonlocal Hamiltonian and symplectic structures,
hierarchies of symmetries, hierarchies of conservation laws, recursion
operators for symmetries and generating functions of conservation laws
(cosymmetries). Highly interesting are the appearances of operators that send
conservation laws and symmetries to each other but are neither Hamiltonian, nor
symplectic. These operators give rise to a noncommutative infinite-dimensional
algebra of recursion operators.


title:
Nonequilibrium transition induced by mass media in a model for social
  influence

abstract:
  We study the effect of mass media, modeled as an applied external field, on a
social system based on Axelrod's model for the dissemination of culture. The
numerical simulations show that the system undergoes a nonequilibrium phase
transition between an ordered phase (homogeneous culture) specified by the mass
media and a disordered (culturally fragmented) one. The critical boundary
separating these phases is calculated on the parameter space of the system,
given by the intensity of the mass media influence and the number of options
per cultural attribute. Counterintuitively, mass media can induce cultural
diversity when its intensity is above some threshold value. The nature of the
phase transition changes from continuous to discontinuous at some critical
value of the number of options.


title:
Soliton solutions of driven non-linear and higher order non-linear
  Schr\"odinger equations

abstract:
  We analyse the structure of the exact, dark and bright soliton solutions of
the driven non-linear Schr\"odinger equation. It is found that, a wide class of
solutions of the higher order non-linear Schr\"odinger equation with a source
can also be obtained through the above procedure. Distinct parameter ranges,
allowing the existence of these solutions, phase locked with their respective
sources, are delineated. Conditions for obtaining non-propagating solutions are
found to be quite different for both the equations. A special case, where the
scale of the soliton emerges as a free parameter, is obtained and the condition
under which solitons can develop singularity is pointed out. We also study the
highly restrictive structure of the localised solutions, when the phase and
amplitude get coupled.


title: Combinatorial Approach to Object Analysis

abstract:
  We present a perceptional mathematical model for image and signal analysis. A
resemblance measure is defined, and submitted to an innovating combinatorial
optimization algorithm. Numerical Simulations are also presented


title: Geometric Diagnostics of Complex Patterns: Spiral Defect Chaos

abstract:
  Motivated by the observation of spiral patterns in a wide range of physical,
chemical, and biological systems we present an approach that aims at
characterizing quantitatively spiral-like elements in complex stripe-like
patterns. The approach provides the location of the spiral tip and the size of
the spiral arms in terms of their arclength and their winding number. In
addition, it yields the number of pattern components (Betti number), as well as
their size and certain aspects of their shape. We apply the method to spiral
defect chaos in thermally driven Rayleigh-B\'enard convection and find that the
arclength of spirals decreases monotonically with decreasing Prandtl number of
the fluid and increasing heating. By contrast, the winding number of the
spirals is non-monotonic in the heating. The distribution function for the
number of spirals is significantly narrower than a Poisson distribution. The
distribution function for the winding number shows approximately an exponential
decay. It depends only weakly on the heating, but strongly on the Prandtl
number. Large spirals arise only for larger Prandtl numbers ($Pr \gtrsim 1$).
In this regime the joint distribution for the spiral length and the winding
number exhibits a three-peak structure indicating the dominance of Archimedean
spirals of opposite sign and relatively straight sections. For small Prandtl
numbers the distribution function reveals a large number of small compact
pattern components.


title:
Pinning and depinning of a classic quasi-one-dimensional Wigner crystal
  in the presence of a constriction

abstract:
  We studied the dynamics of a quasi-one-dimensional chain-like system of
charged particles at low temperature, interacting through a screened Coulomb
potential in the presence of a local constriction. The response of the system
when an external electric field is applied was investigated. We performed
Langevin molecular dynamics simulations for different values of the driving
force and for different temperatures. We found that the friction together with
the constriction pins the particles up to a critical value of the driving
force. The system can depin \emph{elastically} or \emph{quasi-elastically}
depending on the strength of the constriction. The elastic (quasi-elastic)
depinning is characterized by a critical exponent $\beta\sim0.66$
($\beta\sim0.95$). The dc conductivity is zero in the pinned regime, it has
non-ohmic characteristics after the activation of the motion and then it is
constant. Furthermore, the dependence of the conductivity with temperature and
strength of the constriction was investigated in detail. We found interesting
differences between the single and the multi-chain regimes as the temperature
is increased.


title: The Role of Redundancy in the Robustness of Random Boolean Networks

abstract:
  Evolution depends on the possibility of successfully exploring fitness
landscapes via mutation and recombination. With these search procedures,
exploration is difficult in "rugged" fitness landscapes, where small mutations
can drastically change functionalities in an organism. Random Boolean networks
(RBNs), being general models, can be used to explore theories of how evolution
can take place in rugged landscapes; or even change the landscapes.
  In this paper, we study the effect that redundant nodes have on the
robustness of RBNs. Using computer simulations, we have found that the addition
of redundant nodes to RBNs increases their robustness. We conjecture that
redundancy is a way of "smoothening" fitness landscapes. Therefore, redundancy
can facilitate evolutionary searches. However, too much redundancy could reduce
the rate of adaptation of an evolutionary process. Our results also provide
supporting evidence in favour of Kauffman's conjecture (Kauffman, 2000, p.195).

categories: nlin.AO cond-mat.stat-mech cs.CC nlin.CG physics.bio-ph q-bio.MN q-bio.QM


title: 2-Soliton-solution of the Novikov-Veselov equation

abstract:
  Based on a superposition method recently proposed to obtain 1-solitary wave
solutions of the KdV-Burgers equation \cite{Yua2005}, we show that this method
can also be used to find a 2-solitary wave solution of the Novikov-Veselov
equation. Thus, it seems that the method of Yuanxi and Jiashi in general is not
restricted to constructing 1-solitary wave solutions of nonlinear wave and
evolution equations (NLWEEs).


title: Eddy diffusivity in convective hydromagnetic systems

abstract:
  An eigenvalue equation, for linear instability modes involving large scales
in a convective hydromagnetic system, is derived in the framework of multiscale
analysis. We consider a horizontal layer with electrically conducting
boundaries, kept at fixed temperatures and with free surface boundary
conditions for the velocity field; periodicity in horizontal directions is
assumed. The steady states must be stable to short (fast) scale perturbations
and possess symmetry about the vertical axis, allowing instabilities involving
large (slow) scales to develop. We expand the modes and their growth rates in
power series in the scale separation parameter and obtain a hierarchy of
equations, which are solved numerically. Second order solvability condition
yields a closed equation for the leading terms of the asymptotic expansions and
respective growth rate, whose origin is in the (combined) eddy diffusivity
phenomenon. For about 10% of randomly generated steady convective hydromagnetic
regimes, negative eddy diffusivity is found.


title: Moving embedded lattice solitons

abstract:
  It was recently proved that isolated unstable "embedded lattice solitons"
(ELS) may exist in discrete systems. The discovery of these ELS gives rise to
relevant questions such as the following: are there continuous families of
ELS?, can ELS be stable?, is it possible for ELS to move along the lattice?,
how do ELS interact?. The present work addresses these questions by showing
that a novel differential-difference equation (a discrete version of a complex
mKdV equation) has a two-parameter continuous family of exact ELS. The
numerical tests reveal that these solitons are stable and robust enough to
withstand collisions. The model may apply to the description of a Bose-Einstein
condensate with dipole-dipole interactions between the atoms, trapped in a deep
optical-lattice potential.


title:
Dynamics of coupled Josephson junctions under the influence of applied
  fields

abstract:
  We investigate the effect of the phase difference of applied fields on the
dynamics of mutually coupled Josephson junction.
  The system desynchronizes for any value of applied phase difference and the
dynamics even changes from chaotic to periodic motion for some values of
applied phase difference. We report that by keeping the value of phase
difference as $\pi$, the system continues to be in periodic motion for a wide
range of system parameter values which might be of great practical
applications.


title:
Lyapunov exponent for inertial particles in the 2D Kraichnan model as a
  problem of Anderson localization with complex valued potential

abstract:
  We exploit the analogy between dynamics of inertial particle pair separation
in a random-in-time flow and the Anderson model of a quantum particle on the
line in a spatially random real-valued potential. Thereby we get an exact
formula for the Lyapunov exponent of pair separation in a special case, and we
are able to generalize the class of solvable models slightly, for potentials
that are real up to a global complex multiplier. A further important result for
inertial particle behavior, supported by analytical computations in some cases
and by numerics more generally, is that of the decay of the Lyapunov exponent
with large Stokes number (quotient of particle relaxation and flow turn-over
time-scales) as Stokes number to the power -2/3.


title: The co-evolutionary dynamics of directed network of spin market agents

abstract:
  The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is
extended into co-evolutionary version, where strategies of interacting and
competitive traders are represented by local and global couplings between the
nodes of dynamic directed stochastic network. The co-evolutionary principles
are applied in the frame of Bak - Sneppen self-organized dynamics [P. Bak, K.
Sneppen, Phys. Rev. Letter 71 (1993) 4083] that includes the processes of
selection and extinction actuated by the local (node) fitness. The local
fitness is related to orientation of spin agent with respect to instant
magnetization. The stationary regime characterized by a fat tailed distribution
of the log-price returns with index $\alpha\simeq 3.6$ (out of the Levy range)
is identified numerically. The non-trivial consequence of the extremal dynamics
is the partially power-law decay (an effective exponent varies between -0.3 and
-0.6) of the autocorrelation function of volatility. Broad-scale network
topology with node degree distribution characterized by the exponent
$\gamma=1.8$ from the range of social networks is obtained.


title:
A note on the Painleve analysis of a (2+1) dimensional Camassa-Holm
  equation

abstract:
  We investigate the Painleve analysis for a (2+1) dimensional Camassa-Holm
equation. Our results show that it admits only weak Painleve expansions. This
then confirms the limitations of the Painleve test as a test for complete
integrability when applied to non-semilinear partial differential equations.


title: Metastability and dispersive shock waves in Fermi-Pasta-Ulam system

abstract:
  We show the relevance of the dispersive analogue of the shock waves in the
FPU dynamics. In particular we give strict numerical evidences that metastable
states emerging from low frequency initial excitations, are indeed constituted
by dispersive shock waves travelling through the chain. Relevant
characteristics of the metastable states, such as their frequency extension and
their time scale of formation, are correctly obtained within this framework,
using the underlying continuum model, the KdV equation.


title: Stickiness of Trajectories in a Perturbed Anosov System

abstract:
  We consider a perturbation of the Anosov-type system, which leads to the
appearance of a hierarchical set of islands-around-islands. We demonstrate by
simulation that the boundaries of the islands are sticky to trajectories. This
phenomenon leads to the distribution of Poincare recurrences with power-like
tails in contrast to the exponential distribution in the Anosov-type systems.


title:
Effect of the Centrifugal Force on Domain Chaos in Rayleigh-B\'enard
  convection

abstract:
  Experiments and simulations from a variety of sample sizes indicated that the
centrifugal force significantly affects rotating Rayleigh-B\'enard
convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state
consisting of domain chaos close to the sample center, surrounded by an annulus
of nearly-stationary nearly-radial rolls populated by occasional defects
reminiscent of undulation chaos. Although the Coriolis force is responsible for
domain chaos, by comparing experiment and simulation we show that the
centrifugal force is responsible for the radial rolls. Furthermore, simulations
of the Boussinesq equations for smaller aspect ratios neglecting the
centrifugal force yielded a domain precession-frequency $f\sim\epsilon^\mu$
with $\mu\simeq1$ as predicted by the amplitude-equation model for domain
chaos, but contradicted by previous experiment. Additionally the simulations
gave a domain size that was larger than in the experiment. When the centrifugal
force was included in the simulation, $\mu$ and the domain size closely agreed
with experiment.


title: The N-soliton solution of the Degasperis-Procesi equation

abstract:
  This paper extends the results of the previous paper designated I hereafter
in which the one- and two-soiton solutions of the Degasperis-Procesi(DP)
equation were obtained and their peakon limit was considered. Here, we present
the general N-soliton solution of the DP equation and investigate its property.
We show that it has a novel structure expressed by a parametric representation
in terms of the BKP tau-functions. A purely algebraic proof of the solution is
given by establishing various identities among the tau-functions. The large
time asymptotic of the solution recovers the formula for the phase shift which
was derived in I by a different method. Finally, the structure of the N-soliton
solution is discussed in comparison with that of the Camassa-Holm shallow water
wave equation.


title:
A Simple and Unified Approach to Identify Integrable Nonlinear
  Oscillators and Systems

abstract:
  In this paper, we consider a generalized second order nonlinear ordinary
differential equation of the form
$\ddot{x}+(k_1x^q+k_2)\dot{x}+k_3x^{2q+1}+k_4x^{q+1}+\lambda_1x=0$, where
$k_i$'s, $i=1,2,3,4$, $\lambda_1$ and $q$ are arbitrary parameters, which
includes several physically important nonlinear oscillators such as the simple
harmonic oscillator, anharmonic oscillator, force-free Helmholtz oscillator,
force-free Duffing and Duffing-van der Pol oscillators, modified Emden type
equation and its hierarchy, generalized Duffing-van der Pol oscillator equation
hierarchy and so on and investigate the integrability properties of this rather
general equation. We identify several new integrable cases for arbitrary value
of the exponent $q, q\in R$. The $q=1$ and $q=2$ cases are analyzed in detail
and the results are generalized to arbitrary $q$. Our results show that many
classical integrable nonlinear oscillators can be derived as sub-cases of our
results and significantly enlarge the list of integrable equations that exist
in the contemporary literature. To explore the above underlying results we use
the recently introduced generalized extended Prelle-Singer procedure applicable
to second order ODEs. As an added advantage of the method we not only identify
integrable regimes but also construct integrating factors, integrals of motion
and general solutions for the integrable cases, wherever possible, and bring
out the mathematical structures associated with each of the integrable cases.


title: Low-dimensional chaos in populations of strongly-coupled noisy maps

abstract:
  We characterize the macroscopic attractor of infinite populations of noisy
maps subjected to global and strong coupling by using an expansion in order
parameters. We show that for any noise amplitude there exists a large region of
strong coupling where the macroscopic dynamics exhibits low-dimensional chaos
embedded in a hierarchically-organized, folded, infinite-dimensional set. Both
this structure and the dynamics occuring on it are well-captured by our
expansion. In particular, even low-degree approximations allow to calculate
efficiently the first macroscopic Lyapunov exponents of the full system.


title:
Long-Range Spectral Statistics of Classically Integrable Systems
  --Investigation along the Line of the Berry-Robnik Approach--

abstract:
  Extending the argument of Ref.\citen{[4]} to the long-range spectral
statistics of classically integrable quantum systems, we examine the level
number variance, spectral rigidity and two-level cluster function. These
observables are obtained by applying the approach of Berry and Robnik\cite{[0]}
and the mathematical framework of Pandey \cite{[2]} to systems with infinitely
many components, and they are parameterized by a single function $\bar{c}$,
where $\bar{c}=0$ corresponds to Poisson statistics, and $\bar{c}\not=0$
indicates deviations from Poisson statistics. This implies that even when the
spectral components are statistically independent, non-Poissonian spectral
statistics are possible.


title: On Difference Equations Motivated by Modelling the Heart

abstract:
  The analytical structure of some generalizations of the circle map is given.
Also a generalization of off centre reflection is studied. The stability of
Ito-Glass coupled map lattice is studied.


title:
Shape changing (intensity redistribution) collisions of solitons in
  mixed coupled nonlinear Schr{\"o}dinger equations

abstract:
  A novel kind of shape changing (intensity redistribution) collision with
potential application to signal amplification is identified in the integrable
$N$-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of
focusing and defocusing type nonlinearity coefficients. The corresponding
soliton solutions for N=2 case are obtained by using Hirota's bilinearization
method. The distinguishing feature of the mixed sign CNLS equations is that the
soliton solutions can both be singular and regular. Although the general
soliton solution admits singularities we present parametric conditions for
which non-singular soliton propagation can occur. The multisoliton solutions
and a generalization of the results to multicomponent case with arbitrary $N$
are also presented. An appealing feature of soliton collision in the present
case is that all the components of a soliton can simultaneously enhance their
amplitudes, which can lead to new kind of amplification process without induced
noise.


title: Second Order Superintegrable Systems in Three Dimensions

abstract:
  A classical (or quantum) superintegrable system on an n-dimensional
Riemannian manifold is an integrable Hamiltonian system with potential that
admits 2n-1 functionally independent constants of the motion that are
polynomial in the momenta, the maximum number possible. If these constants of
the motion are all quadratic, the system is second order superintegrable. Such
systems have remarkable properties. Typical properties are that 1) they are
integrable in multiple ways and comparison of ways of integration leads to new
facts about the systems, 2) they are multiseparable, 3) the second order
symmetries generate a closed quadratic algebra and in the quantum case the
representation theory of the quadratic algebra yields important facts about the
spectral resolution of the Schr\"odinger operator and the other symmetry
operators, and 4) there are deep connections with expansion formulas relating
classes of special functions and with the theory of Exact and Quasi-exactly
Solvable systems. For n=2 the author, E.G. Kalnins and J. Kress, have worked
out the structure of these systems and classified all of the possible spaces
and potentials. Here I discuss our recent work and announce new results for the
much more difficult case n=3.


title: Matter-wave solitons supported by dissipation

abstract:
  We show how novel types of long-lived self-localized matter waves can be
constructed with Bose-Einstein condensates. The ingredients leading to such
structures are a spatial phase generating a flux of atoms towards the
condensate center and the dissipative mechanism provided by the inelastic
three-body collisions in atomic Bose-Einstein condensates. The outcome is an
striking example of nonlinear structure supported by dissipation.


title:
Effects of microscopic disorder on the collective dynamics of globally
  coupled maps

abstract:
  This paper studies the effect of independent additive noise on the
synchronous dynamics of large populations of globally coupled maps. Our
analysis is complementary to the approach taken by Teramae and Kuramoto
[Teramae and Kuramoto, Phys. Rev. E 63:036210, 2001] who pointed out the
anomalous scaling properties preceding the loss of coherence. We focus on the
macroscopic dynamics that remains deterministic at any noise level and differs
from the microscopic one. Using properly defined order parameters, an
analytical approach is proposed for describing the collective dynamics in terms
of an approximate low-dimensional system. The systematic derivation of the
macroscopic equations provides a link between the microscopic features of the
population (single-element dynamics and noise distribution) and the properties
of the emergent behaviour. The macroscopic bifurcations induced by noise are
compared to those originating from parameter mismatches within the population.


title:
Power and power-logarithmic expansions for travelling-wave solutions of
  the Burgers-Huxley equation

abstract:
  The Burgers-Huxley equation is studied. All power and power-logarithmic
expansions for travelling-wave solutions of this equation are presented. Using
the power expansions, some exact solutions of this equation are found.


title: A Gentle (without Chopping) Approach to the Full Kostant-Toda Lattice

abstract:
  In this paper we propose a new algorithm for obtaining the rational integrals
of the full Kostant-Toda lattice. This new approach is based on a reduction of
a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the
space of maps from Z_n to GL(n,R) endowed with a structure of a pair of
Lie-algebroids.


title:
Distributed Sources, Accelerated Universe, Consciousness and Quantum
  Entanglement

abstract:
  It is shown that such diverse phenomena as accelerated Universe,
consciousness and quantum entanglement are connected by the concept of
distributed sources and imaginary (particularly, tachyon) fields.


title:
Real-time update of multi-fractal analysis on dynamic time series using
  incremental discrete wavelet transforms

abstract:
  An algorithm is presented to update the multi-fractal spectrum of a time
series in constant time when new data arrives. The discrete wavelet transform
(DWT) of the time series is first updated for the new data value. This is done
optimally in terms of sharing previous computations, in O(L) constant time,
with L the number of levels of decomposition. The multi-fractal spectrum is
then updated also in constant-time. New pre-computation techniques are
presented to further accelerate this process. All possible 2^L data alignments
are taken into account in the course of the incremental updates. The resulting
spectrum estimate is more stable, compared to the current DWT method using only
one dyadic frame, as precise, and more efficient. It is adapted for real-time
on-line updates of the time series.


title:
Poisson-to-Wigner crossover transition in the nearest-neighbor spacing
  statistics of random points on fractals

abstract:
  We show that the nearest-neighbor spacing distribution for a model that
consists of random points uniformly distributed on a self-similar fractal is
the Brody distribution of random matrix theory. In the usual context of
Hamiltonian systems, the Brody parameter does not have a definite physical
meaning, but in the model considered here, the Brody parameter is actually the
fractal dimension. Exploiting this result, we introduce a new model for a
crossover transition between Poisson and Wigner statistics: random points on a
continuous family of self-similar curves with fractal dimension between 1 and
2. The implications to quantum chaos are discussed, and a connection to
conservative classical chaos is introduced.


title: Ansatz of Hans Bethe for a two-dimensional Bose gas

abstract:
  The method of q-oscillator lattices, proposed recently in [hep-th/0509181],
provides the tool for a construction of various integrable models of quantum
mechanics in 2+1 dimensional space-time. In contrast to any one dimensional
quantum chain, its two dimensional generalizations -- quantum lattices -- admit
different geometrical structures. In this paper we consider the q-oscillator
model on a special lattice. The model may be interpreted as a two-dimensional
Bose gas. The most remarkable feature of the model is that it allows the
coordinate Bethe Ansatz: the p-particles' wave function is the sum of plane
waves. Consistency conditions is the set of 2p equations for p one-particle
wave vectors. These "Bethe Ansatz" equations are the main result of this paper.


title: Clustering of floaters by waves

abstract:
  We study experimentally how waves affect distribution of particles that float
on a water surface. We show that clustering of small particles in a standing
wave is a nonlinear effect with the clustering time decreasing as the square of
the wave amplitude. In a set of random waves, we show that small floaters
concentrate on a multi-fractal set.


title:
Power and non-power expansions of the solutions for the fourth-order
  analogue to the second Painlev\'{e} equation

abstract:
  Fourth - order analogue to the second Painlev\'{e} equation is studied. This
equation has its origin in the modified Korteveg - de Vries equation of the
fifth order when we look for its self - similar solution. All power and non -
power expansions of the solutions for the fouth - order analogue to the second
Painlev\'{e} equation near points $z=0$ and $z=\infty$ are found by means of
the power geometry method. The exponential additions to solutions of the
equation studied are determined. Comparison of the expansions found with those
of the six Painlev\'{e} equations confirm the conjecture that the fourth -
order analogue to the second Painlev\'{e} equation defines new transcendental
functions.


title:
Exponential Recovery of Low Frequency Fluctuations in a Diode Laser with
  Optical Feedback

abstract:
  We show that the recovery after each power drop on the chaotic Low Frequency
Fluctuations in a semiconductor laser with optical feedback follows an
exponential envelope. The time constant for such exponential behavior was
experimentally measured. This recovery time constant and the average time
interval between consecutive drops are shown to have different dependences when
measured as function of the pump current.


title: The Perturbed NLS Equation and Asymptotic Integrability

abstract:
  The perturbed NLS equation is asymptotically integrable if the zero-order
approximation to the solution is a single soliton. It is not integrable for any
other zero-order solution. In the standard application of a Normal Form
expansion, integrability is recovered if, from second order onwards, the
perturbation obeys algebraic constraints. In general, these are not satisfied.
As a result, the Normal Form is not asymptotically integrable; its solution,
the zero-order approximation, loses the simple structure of the solution of the
unperturbed equation. This work exploits the freedom in the perturbative
expansion to propose an alternative, for which the loss of integrability only
affects higher-order terms in the expansion of the solution. The Normal Form
remains asymptotically integrable, and the zero-order approximation, not
affected by the loss of integrability, has the same structure as the solution
of the unperturbed equation. In the case of a multiple-soliton zero-order
approximation, the loss of integrability affects the higher-order corrections
to the solution in a finite domain around the origin in the x-t plane, the
soliton interaction region. The effect decays exponentially in all directions
in the plane as the distance from the origin grows. The computation is carried
through second order.


title: Persistence Probabilities of the German DAX and Shanghai Index

abstract:
  We present a relatively detailed analysis of the persistence probability
distributions in financial dynamics. Compared with the auto-correlation
function, the persistence probability distributions describe dynamic
correlations non-local in time. Universal and non-universal behaviors of the
German DAX and Shanghai Index are analyzed, and numerical simulations of some
microscopic models are also performed. Around the fixed point $z_0=0$, the
interacting herding model produces the scaling behavior of the real markets.


title: KdV Surfaces

abstract:
  We consider 2-surfaces arising from the Korteweg de Vries (KdV) equation. The
surfaces corresponding to KdV are in a three dimensional Minkowski space. They
contain a family of quadratic Weingarten and Willmore-like surfaces. We show
that a subset of KdV surfaces can be obtained from a variational principle
where the Lagrange function is a polynomial function of the Gaussian and mean
curvatures. We finally give a method for constructing the surfaces explicitly,
i.e., finding their parametrizations or finding their position vectors.

categories: nlin.SI gr-qc hep-th math-ph math.DG math.MP


title:
Destruction of adiabatic invariance at resonances in slow-fast
  Hamiltonian systems

abstract:
  There are many problems that lead to analysis of dynamical systems in which
one can distinguish motions of two types: slow one and fast one. An averaging
over fast motion is used for approximate description of the slow motion. First
integrals of the averaged system are approximate first integrals of the exact
system, i.e. adiabatic invariants. Resonant phenomena in fast motion (capture
into resonance, scattering on resonance) lead to inapplicability of averaging,
destruction of adiabatic invariance, dynamical chaos and transport in large
domains in the phase space. In the paper perturbation theory methods for
description of these phenomena are outlined. We also consider as an example the
problem of surfatron acceleration of a relativistic charged particle.


title:
On the extended resolvent of the Nonstationary Schrodingher operator for
  a Darboux transformed potential

abstract:
  In the framework of the resolvent approach it is introduced a so called
twisting operator that is able, at the same time, to superimpose \`a la Darboux
$N$ solitons to a generic smooth decaying potential of the Nonstationary
Schr\"odinger operator and to generate the corresponding Jost solutions. This
twisting operator is also used to construct an explicit bilinear representation
in terms of the Jost solutions of the related extended resolvent. The main
properties of the Jost and auxiliary Jost solutions and of the resolvent are
discussed.


title: Multidimensional semi-gap solitons in a periodic potential

abstract:
  The existence, stability and other dynamical properties of a new type of
multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional
(1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger
equation with the self-defocusing cubic nonlinearity are studied. The equation
describes propagation of light in a medium with normal group-velocity
dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its
spectrum does not support a true bandgap. Nevertheless, the variational
approximation (VA) and numerical computations reveal stable solutions that seem
as completely localized ones, an explanation to which is given. The solutions
are of the gap-soliton type in the transverse direction(s), in which the
periodic potential acts in combination with the diffraction and self-defocusing
nonlinearity. Simultaneously, in the longitudinal (temporal) direction these
are ordinary solitons, supported by the balance of the normal GVD and
defocusing nonlinearity. Stability of the solitons is predicted by the VA, and
corroborated by direct simulations.


title:
Crossover from self-defocusing to discrete trapping in nonlinear
  waveguide arrays

abstract:
  We predict a sharp crossover from nonlinear self-defocusing to discrete
self-trapping of a narrow Gaussian beam with the increase of the refractive
index contrast in a periodic photonic lattice. We demonstrate experimentally
nonlinear discrete localization of light with defocusing nonlinearity by single
site excitation in LiNbO$_3$ waveguide arrays.


title: Localized states in bistable pattern forming systems

abstract:
  We present an unifying description of a new class of localized states,
appearing as large amplitude peaks nucleating over a pattern of lower
amplitude. Localized states are pinned over a lattice spontaneously generated
by the system itself. We show that the phenomenon is generic and requires only
the coexistence of two spatially periodic states. At the onset of the spatial
bifurcation, a forced amplitude equation is derived for the critical modes,
which accounts for the appearance of localized peaks


title: Ermakov's Superintegrable Toy and Nonlocal Symmetries

abstract:
  We investigate the symmetry properties of a pair of Ermakov equations. The
system is superintegrable and yet possesses only three Lie point symmetries
with the algebra sl(2,R). The number of point symmetries is insufficient and
the algebra unsuitable for the complete specification of the system. We use the
method of reduction of order to reduce the nonlinear fourth-order system to a
third-order system comprising a linear second-order equation and a conservation
law. We obtain the representation of the complete symmetry group from this
system. Four of the required symmetries are nonlocal and the algebra is the
direct sum of a one-dimensional Abelian algebra with the semidirect sum of a
two-dimensional solvable algebra with a two-dimensional Abelian algebra. The
problem illustrates the difficulties which can arise in very elementary
systems. Our treatment demonstrates the existence of possible routes to
overcome these problems in a systematic fashion.


title:
On weakly non-local, nilpotent, and super-recursion operators for N=1
  super-equations

abstract:
  We consider nonlinear, scaling-invariant N=1 boson + fermion supersymmetric
systems whose right-hand sides are homogeneous differential polynomials and
satisfy some natural assumptions. We select the super-systems that admit
infinitely many higher symmetries generated by recursion operators; we further
restrict ourselves to the case when the dilaton dimensions of the bosonic and
fermionic super-fields coincide and the weight of the time is half the weight
of the spatial variable.
  We discover five systems that satisfy these assumptions; one system is
transformed to the purely bosonic Burgers equation. We construct local,
nilpotent, triangular, weakly non-local, and super-recursion operators for
their symmetry algebras.


title: Discrete Dynamical Systems Embedded in Cantor Sets

abstract:
  While the notion of chaos is well established for dynamical systems on
manifolds, it is not so for dynamical systems over discrete spaces with $ N $
variables, as binary neural networks and cellular automata. The main difficulty
is the choice of a suitable topology to study the limit $N\to\infty$. By
embedding the discrete phase space into a Cantor set we provided a natural
setting to define topological entropy and Lyapunov exponents through the
concept of error-profile. We made explicit calculations both numerical and
analytic for well known discrete dynamical models.


title: Noether Symmetries and Critical Exponents

abstract:
  We show that all Lie point symmetries of various classes of nonlinear
differential equations involving critical nonlinearities are
variational/divergence symmetries.


title:
The influence of quantum field fluctuations on chaotic dynamics of
  Yang-Mills system II. The role of the centrifugal term

abstract:
  We have considered SU(2)xU(1) gauge field theory describing electroweak
interactions. We have demonstrated that centrifugal term in model Hamiltonian
increases the region of regular dynamics of Yang-Mills and Higgs fields system
at low densities of energy. Also we have found analytically the approximate
relation for critical density of energy of the order to chaos transition on
centrifugal constant. It is necessary to note that mentioned increase of the
region of regular dynamics has linear dependance on the value of the
centrifugal constant.


title:
Stability of Yang-Mills-Higgs field system in the homogeneous self-dual
  vacuum field

abstract:
  Classical dynamics of SU(2) model gauge field system with Higgs field is
considered in the homogeneous nonperturbative self-dual vacuum field. The
regions of instability in parametric space are detected and described
analytically.


title:
Self-synchronization of Cellular Automata: an attempt to control
  patterns

abstract:
  The searching for the stable patterns in the evolution of cellular automata
is implemented using stochastic synchronization between the present structures
of the system and its precedent configurations. For most of the known evolution
rules with complex behavior a dynamic competition among all the possible stable
patterns is established and no stationary regime is reached. For the particular
rule coded by the decimal number 18, a self-synchronization phenomenon can be
obtained, even when strong modifications to the synchronization method are
applied.


title:
From St\"{a}ckel systems to integrable hierarchies of PDE's: Benenti
  class of separation relations

abstract:
  We propose a general scheme of constructing of soliton hierarchies from
finite dimensional St\"{a}ckel systems and related separation relations. In
particular, we concentrate on the simplest class of separation relations,
called Benenti class, i.e. certain St\"{a}ckel systems with quadratic in
momenta integrals of motion.


title:
Geometry-induced pulse instability in microdesigned catalysts: the
  effect of boundary curvature

abstract:
  We explore the effect of boundary curvature on the instability of reactive
pulses in the catalytic oxidation of CO on microdesigned Pt catalysts. Using
ring-shaped domains of various radii, we find that the pulses disappear
(decollate from the inert boundary) at a turning point bifurcation, and trace
this boundary in both physical and geometrical parameter space. These
computations corroborate experimental observations of pulse decollation.


title: Domain wall dynamics in expanding spaces

abstract:
  We study the effects on the dynamics of kinks due to expansions and
contractions of the space. We show that the propagation velocity of the kink
can be adiabatically tuned through slow expansions/contractions, while its
width is given as a function of the velocity. We also analyze the case of fast
expansions/contractions, where we are no longer on the adiabatic regime. In
this case the kink moves more slowly after an expansion-contraction cycle as a
consequence of loss of energy through radiation. All these effects are
numerically studied in the nonlinear Klein-Gordon equations (both for the
sine-Gordon and for the phi^4 potential), and they are also studied within the
framework of the collective coordinate evolution equations for the width and
the center of mass of the kink. These collective coordinate evolution equations
are obtained with a procedure that allows us to consider even the case of large
expansions/contractions.


title:
The Domain Chaos Puzzle and the Calculation of the Structure Factor and
  Its Half-Width

abstract:
  The disagreement of the scaling of the correlation length xi between
experiment and the Ginzburg-Landau (GL) model for domain chaos was resolved.
The Swift-Hohenberg (SH) domain-chaos model was integrated numerically to
acquire test images to study the effect of a finite image-size on the
extraction of xi from the structure factor (SF). The finite image size had a
significant effect on the SF determined with the Fourier-transform (FT) method.
The maximum entropy method (MEM) was able to overcome this finite image-size
problem and produced fairly accurate SFs for the relatively small image sizes
provided by experiments.
  Correlation lengths often have been determined from the second moment of the
SF of chaotic patterns because the functional form of the SF is not known.
Integration of several test functions provided analytic results indicating that
this may not be a reliable method of extracting xi. For both a Gaussian and a
squared SH form, the correlation length xibar=1/sigma, determined from the
variance sigma^2 of the SF, has the same dependence on the control parameter
epsilon as the length xi contained explicitly in the functional forms. However,
for the SH and the Lorentzian forms we find xibar ~ xi^1/2.
  Results for xi determined from new experimental data by fitting the
functional forms directly to the experimental SF yielded xi ~ epsilon^-nu} with
nu ~= 1/4 for all four functions in the case of the FT method, but nu ~= 1/2,
in agreement with the GL prediction, in the the case of the MEM. Over a wide
range of epsilon and wave number k, the experimental SFs collapsed onto a
unique curve when appropriately scaled by xi.


title: Fractional and fractal derivatives modeling of turbulence

abstract:
  This study makes the first attempt to use the 2/3-order fractional Laplacian
modeling of enhanced diffusing movements of random turbulent particle resulting
from nonlinear inertial interactions. A combined effect of the inertial
interactions and the molecule Brownian diffusivities is found to be the
bi-fractal mechanism behind multifractal scaling in the inertial range of
scales of moderate Reynolds number turbulence. Accordingly, a stochastic
equation is proposed to describe turbulence intermittency. The 2/3-order
fractional Laplacian representation is also used to construct a fractional
Reynolds equation for nonlinear interactions of fluctuating velocity
components, underlying turbulence spacetime fractal structures of Levy 2/3
stable distribution. The new perspective of this study is that the fractional
calculus is an effective approach modeling of chaotic fractal phenomena induced
by nonlinear interactions.


title:
Classification of the solutions of constant rational semi-dynamical
  reflection equations

abstract:
  We propose a classification of the solutions K to the semi-dynamical
reflection equation with constant rational structure matrices associated to
rational scalar Ruijsenaars-Schneider model. Four sets of solutions are
identified and simple analytic transformations generate all solutions from
these sets.


title: Soliton solutions of the Kadomtsev-Petviashvili II equation

abstract:
  We study a general class of line-soliton solutions of the
Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form
of its tau-function. We show that, in addition to previously known line-soliton
solutions, this class also contains a large variety of new multi-soliton
solutions, many of which exhibit nontrivial spatial interaction patterns. We
also show that, in general, such solutions consist of unequal numbers of
incoming and outgoing line solitons. From the asymptotic analysis of the
tau-function, we explicitly characterize the incoming and outgoing
line-solitons of this class of solutions. We illustrate these results by
discussing several examples.


title: On the models of nonlocal nonlinear optics

abstract:
  We show that under certain assumptions a general model of nonlocal nonlinear
response in 1+1-dimension is equivalent to the model considered by Krolikowski
and Bang for a Kerr-type medium. We derive the limit of weak nonlocality in
high frequency regime and discuss the integrable cases.


title: Dynamical Systems as Logic Gates

abstract:
  A scheme for logical computation using non-linear dynamical systems is
presented. Examples of discrete-time maps configured as AND, OR, NAND and NOR
gates are given. It is seen that the logical operations are flexible in the
sense that an AND gate can be transformed into an OR gate with a simple change
of a single parameter and vice-versa. Also, a NAND gate can be transformed into
a NOR gate and vice-versa. It is shown, by example, that the scheme can even be
extended to continuous-time flows. Since the NAND and NOR operations are
universal, it is possible to implement any switching function by
interconnecting blocks that realize these operations.


title: Approximating multi-dimensional Hamiltonian flows by billiards

abstract:
  Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit
$\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional
billiard. We define auxiliary billiard domains that asymptote, as
$\epsilon\to0$ to the original billiard, and provide asymptotic expansion of
the smooth Hamiltonian solution in terms of these billiard approximations. The
asymptotic expansion includes error estimates in the $C^{r}$ norm and an
iteration scheme for improving this approximation. Applying this theory to
smooth potentials which limit to the multi-dimensional close to ellipsoidal
billiards, we predict when the separatrix splitting persists for various types
of potentials.


title: Connectivity and Cost Trade-offs in Multihop Wireless Networks

abstract:
  Ad-hoc wireless networks are of increasing importance in communication and
are frequently constrained by energy use. Here we propose a distributed,
non-hierarchical adaptive method using preferential detachment for adjusting
node transmission power to reduce overall power consumption without violating
network load limitations. We derive a cost and path length trade-off diagram
that establishes the bounds of effectiveness of the adaptive strategy and
compare it with uniform node transmission strategy for several node topologies.
We achieve cost savings as high as 90% for specific topologies.


title: Laplace Invariants of Toda Lattices with the Exceptional Cartan Matrices

abstract:
  We show that Toda lattices with the exceptional Cartan matrices are Liouville
type systems. For these systems of equations, we obtain explicit formulas for
the invariants and generalized Laplace invariants.


title:
Can quantum fractal fluctuations be observed in an atom-optics kicked
  rotor experiment?

abstract:
  We investigate the parametric fluctuations in the quantum survival
probability of an open version of the delta-kicked rotor model in the deep
quantum regime. Spectral arguments [Guarneri I and Terraneo M 2001 Phys. Rev. E
vol. 65 015203(R)] predict the existence of parametric fractal fluctuations
owing to the strong dynamical localisation of the eigenstates of the kicked
rotor. We discuss the possibility of observing such dynamically-induced
fractality in the quantum survival probability as a function of the kicking
period for the atom-optics realisation of the kicked rotor. The influence of
the atoms' initial momentum distribution is studied as well as the dependence
of the expected fractal dimension on finite-size effects of the experiment,
such as finite detection windows and short measurement times. Our results show
that clear signatures of fractality could be observed in experiments with cold
atoms subjected to periodically flashed optical lattices, which offer an
excellent control on interaction times and the initial atomic ensemble.


title:
Inverse Scattering Transform for the Toda Hierarchy with Quasi-Periodic
  Background

abstract:
  We provide a rigorous treatment of the inverse scattering transform for the
entire Toda hierarchy in the case of a quasi-periodic finite-gap background
solution.


title:
Certain integrable system on a space associated with a quantum search
  algorithm

abstract:
  On thinking of a Grover-type quantum search algorithm for an ordered tuple of
multi-qubit states, a gradient system associated with the negative von-Neumann
entropy is studied on the space of regular relative-configurations of
multi-qubit states (SR${}^2$CMQ). The SR${}^2$CMQ emerges, through a geometric
procedure, from the space of ordered tuples of multi-qubit states for the
quantum search. The aim of this paper is to give a brief report on the
integrability of the gradient dynamical system together with quantum
information geometry of the underlying space, SR${}^2$CMQ, of that system.


title: A New Proof on Net Upscale Energy Cascade in 2D and QG Turbulence

abstract:
  A general proof that more energy flows upscale than downscale in
two-dimensional (2D) turbulence and barotropic quasi-geostrophic (QG)
turbulence is given. A proof is also given that in Surface QG turbulence, the
reverse is true. Though some of these results are known in restricted cases,
the proofs given here are pedagogically simpler, require fewer assumptions and
apply to both forced and unforced cases.


title: Diffusion induced mode switching in avalanching systems

abstract:
  Most avalanching systems in nature should involve diffusive processes as well
which can change the behavior of such systems and should be taken into account.
We examine the effects of diffusion on the model of a dissipative
bi-directional burning model. It is shown that the system behavior
progressively changes with the increase of diffusion. Avalanches of small sizes
become suppressed and large quasiperiodic bursts develop. In contrast with
sandpiles these bursts are not edge triggered and the transition is gradual.


title:
Impeded inverse energy transfer in the Charney--Hasegawa--Mima model of
  quasi-geostrophic flows

abstract:
  The behaviour of turbulent flows within the single-layer quasi-geostrophic
(Charney--Hasegawa--Mima) model is shown to be strongly dependent on the Rossby
deformation wavenumber $\lambda$ (or free-surface elasticity). Herein, we
derive a bound on the inverse energy transfer, specifically on the growth rate
$\d\ell/\dt$ of the characteristic length scale $\ell$ representing the energy
centroid. It is found that $\d\ell/\dt\le2\norm q_\infty/(\ell_s\lambda^2)$,
where $\norm q_\infty$ is the supremum of the potential vorticity and $\ell_s$
represents the potential enstrophy centroid of the reservoir, both invariant.
This result implies that in the potential energy dominated regime
($\ell\ge\ell_s\gg\lambda^{-1}$), the inverse energy transfer is strongly
impeded, in the sense that under the usual time scale no significant transfer
of energy to larger scales occurs. The physical implication is that the
elasticity of the free surface impedes turbulent energy transfer in wavenumber
space, effectively rendering large-scale vortices long-lived and inactive.
Results from numerical simulations of forced-dissipative turbulence confirm
this prediction.


title: Loewner equations and dispersionless hierarchies

abstract:
  Reduction of a dispersionless type integrable system (dcmKP hierarchy) to the
radial Loewner equation is presented.


title:
Universal behavior in populations composed of excitable and
  self-oscillatory elements

abstract:
  We study the robustness of self-sustained oscillatory activity in a globally
coupled ensemble of excitable and oscillatory units. The critical balance to
achieve collective self-sustained oscillations is analytically established. We
also report a universal scaling function for the ensemble's mean frequency. Our
results extend the framework of the `Aging Transition' [Phys. Rev. Lett. 93,
104101 (2004)] including a broad class of dynamical systems potentially
relevant in biology.


title: Nonlinear Fractional Dynamics on a Lattice with Long Range Interactions

abstract:
  A unified approach has been developed to study nonlinear dynamics of a 1D
lattice of particles with long-range power-law interaction. A classical case is
treated in the framework of the generalization of the well-known
Frenkel-Kontorova chain model for the non-nearest interactions. Quantum
dynamics is considered following Davydov's approach for molecular excitons. In
the continuum limit the problem is reduced to dynamical equations with
fractional derivatives resulting from the fractional power of the long-range
interaction. Fractional generalizations of the sine-Gordon, nonlinear
Schrodinger, and Hilbert-Schrodinger equations have been found. There exists a
critical value of the power s of the long-range potential. Below the critical
value (s<3) we obtain equations with fractional derivatives while for s>3 we
have the well-known nonlinear dynamical equations with space derivatives of
integer order. Long-range interaction impact on the quantum lattice propagator
has been studied. We have shown that the quantum exciton propagator exhibits
transition from the well-known Gaussian-like behavior to a power-law decay due
to the long-range interaction. A link between 1D quantum lattice dynamics in
the imaginary time domain and a random walk model has been discussed.


title: On a liquid drop "falling" inside a heavier miscible fluid

abstract:
  We report a new type of drop instability, where the density difference
between the drop and the solvent is negative. We show that the drop falls
inside the solvent down to a minimum height, then fragmentation takes place and
secondary droplets rise up to the surface. We have developed a theoretical
model that captures the essential of the phenomenon and predicts the correct
scalings for the rise-up time and the minimum height.


title: Symmetry Properties of Autonomous Integrating Factors

abstract:
  We study the symmetry properties of autonomous integrating factors from an
algebraic point of view. The symmetries are delineated for the resulting
integrals treated as equations and symmetries of the integrals treated as
functions or configurational invariants. The succession of terms (pattern) is
noted. The general pattern for the solution symmetries for equations in the
simplest form of maximal order is given and the properties of the associated
integrals resulting from this analysis are given.


title: Fractional dynamics of coupled oscillators with long-range interaction

abstract:
  We consider one-dimensional chain of coupled linear and nonlinear oscillators
with long-range power-wise interaction. The corresponding term in dynamical
equations is proportional to $1/|n-m|^{\alpha+1}$. It is shown that the
equation of motion in the infrared limit can be transformed into the medium
equation with the Riesz fractional derivative of order $\alpha$, when
$0<\alpha<2$. We consider few models of coupled oscillators and show how their
synchronization can appear as a result of bifurcation, and how the
corresponding solutions depend on $\alpha$. The presence of fractional
derivative leads also to the occurrence of localized structures. Particular
solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear
Schrodinger) equation are derived. These solutions are interpreted as
synchronized states and localized structures of the oscillatory medium.

categories: nlin.PS cond-mat.stat-mech math-ph math.MP nlin.AO nlin.CD physics.class-ph


title: Use the information dimension, not the Hausdorff

abstract:
  Multi-fractal patterns occur widely in nature. In developing new algorithms
to determine multi-fractal spectra of experimental data I am lead to the
conclusion that generalised dimensions $D_q$ of order $q\leq0$, including the
Hausdorff dimension, are effectively \emph{irrelevant}. The reason is that
these dimensions are extraordinarily sensitive to regions of low density in the
multi-fractal data. Instead, one should concentrate attention on generalised
dimensions $D_q$ for $q\geq 1$, and of these the information dimension $D_1$
seems the most robustly estimated from a finite amount of data.


title: A Predictive Theory of Games

abstract:
  Conventional noncooperative game theory hypothesizes that the joint strategy
of a set of players in a game must satisfy an "equilibrium concept". All other
joint strategies are considered impossible; the only issue is what equilibrium
concept is "correct". This hypothesis violates the desiderata underlying
probability theory. Indeed, probability theory renders moot the problem of what
equilibrium concept is correct - every joint strategy can arise with non-zero
probability. Rather than a first-principles derivation of an equilibrium
concept, game theory requires a first-principles derivation of a distribution
over joint (mixed) strategies. This paper shows how information theory can
provide such a distribution over joint strategies. If a scientist external to
the game wants to distill such a distribution to a point prediction, that
prediction should be set by decision theory, using their (!) loss function. So
the predicted joint strategy - the "equilibrium concept" - varies with the
external scientist's loss function. It is shown here that in many games, having
a probability distribution with support restricted to Nash equilibria - as
stipulated by conventional game theory - is impossible. It is also show how to:
i) Derive an information-theoretic quantification of a player's degree of
rationality; ii) Derive bounded rationality as a cost of computation; iii)
Elaborate the close formal relationship between game theory and statistical
physics; iv) Use this relationship to extend game theory to allow
stochastically varying numbers of players.

categories: nlin.AO cond-mat.stat-mech cs.GT math.GM math.PR


title: Integrable Hierarchy of Higher Nonlinear Schr\"odinger Type Equations

abstract:
  Addition of higher nonlinear terms to the well known integrable nonlinear
Schr\"odinger (NLS) equations, keeping the same linear dispersion (LD) usually
makes the system nonintegrable. We present a systematic method through a novel
Eckhaus-Kundu hierarchy, which can generate higher nonlinearities in the NLS
and derivative NLS equations preserving their integrability. Moreover, similar
nonlinear integrable extensions can be made again in a hierarchical way for
each of the equations in the known integrable NLS and derivative NLS
hierarchies with higher order LD, without changing their LD.

categories: nlin.SI cond-mat.stat-mech hep-th math-ph math.MP


title: Symmetry pattern transition in cellular automata with complex behavior

abstract:
  A transition from asymmetric to symmetric patterns in time-dependent extended
systems is described. It is found that one dimensional cellular automata,
started from fully random initial conditions, can be forced to evolve into
complex symmetrical patterns by stochastically coupling a proportion $p$ of
pairs of sites located at equal distance from the center of the lattice. A
nontrivial critical value of $p$ must be surpassed in order to obtain
symmetrical patterns during the evolution. This strategy is able to classify
the cellular automata rules -with complex behavior- between those that support
time-dependent symmetric patterns and those which do not support such kind of
patterns.


title:
Parametrically controlling solitary wave dynamics in modified Kortweg-de
  Vries equation

abstract:
  We demonstrate the control of solitary wave dynamics of modified Kortweg-de
Vries (MKdV) equation through the temporal variations of the distributed
coefficients. This is explicated through exact cnoidal wave and localized
soliton solutions of the MKdV equation with variable coefficients. The solitons
can be accelerated and their propagation can be manipulated by suitable
variations of the above parameters. In sharp contrast with nonlinear
Schr\"{o}dinger equation, the soliton amplitude and widths are time
independent.


title: Guiding chemical pulses through geometry: Y-junctions

abstract:
  We study computationally and experimentally the propagation of chemical
pulses in complex geometries.The reaction of interest, CO oxidation, takes
place on single crystal Pt(110) surfaces that are microlithographically
patterned; they are also addressable through a focused laser beam, manipulated
through galvanometer mirrors, capable of locally altering the crystal
temperature and thus affecting pulse propagation. We focus on sudden changes in
the domain shape (corners in a Y-junction geometry) that can affect the pulse
dynamics; we also show how brief, localized temperature perturbations can be
used to control reactive pulse propagation.The computational results are
corroborated through experimental studies in which the pulses are visualized
using Reflection Anisotropy Microscopy.


title:
Modulational instability, solitons and periodic waves in models of
  quantum degenerate Boson-Fermion mixtures

abstract:
  In this paper we study a system of coupled nonlinear Schrodinger equations
modelling a quantum degenerate mixture of bosons and fermions. We analyze the
stability of plane waves, give precise conditions for the existence of solitons
and write explicit solutions in the form of periodic waves. We also check that
the solitons observed previously in numerical simulations of the model
correspond exactly to our explicit solutions and see how plane waves
destabilize to form periodic waves.


title: Conservation Laws of Discrete Korteweg-de Vries Equation

abstract:
  All three-point and five-point conservation laws for the discrete Korteweg-de
Vries equations are found. These conservation laws satisfy a functional
equation, which we solve by reducing it to a system of partial differential
equations. Our method uses computer algebra intensively, because the
determining functional equation is quite complicated.


title: Multi-Scale Gradient Expansion of the Turbulent Stress Tensor

abstract:
  We develop an expansion of the turbulent stress tensor into a double series
of contributions from different scales of motion and different orders of
space-derivatives of velocity, a Multi-Scale Gradient (MSG) expansion. The
expansion is proved to converge to the exact stress, as a consequence of the
locality of cascade both in scale and in space. Simple estimates show, however,
that the convergence rate may be slow for the expansion in spatial gradients of
very small scales. Therefore, we develop an approximate expansion, based upon
an assumption that similar or `coherent' contributions to turbulent stress are
obtained from disjoint subgrid regions. This Coherent-Subregions Approximation
(CSA) yields an MSG expansion that can be proved to converge rapidly at all
scales and is hopefully still reasonably accurate. As an application, we
consider the cascades of energy and helicity in three-dimensional turbulence.
To first order in velocity-gradients, the stress has three contributions: a
tensile stress along principal directions of strain, a contractile stress along
vortex lines, and a shear stress proportional to `skew-strain.' While
vortex-stretching plays the major role in energy cascade, there is a second,
less scale-local contribution from `skew-strain'. For helicity cascade the
situation is reversed, and it arises scale-locally from `skew-strain' while the
stress along vortex-lines gives a secondary, less scale-local contribution.
These conclusions are illustrated with simple exact solutions of 3D Euler
equations. In the first, energy cascade occurs by Taylor's mechanism of
stretching and spin-up of small-scale vortices due to large-scale strain. In
the second, helicity cascade occurs by `twisting' of small-scale vortex
filaments due to a large-scale screw.


title:
A Turbulent Constitutive Law for the Two-Dimensional Inverse Energy
  Cascade

abstract:
  We develop a fundamental approach to a turbulent constitutive law for the 2D
inverse cascade, based upon a convergent multi-scale gradient (MSG) expansion.
To first order in gradients we find that the turbulent stress generated by
small-scale eddies is proportional not to strain but instead to `skew-strain,'
i.e. the strain tensor rotated by $45^\circ.$ The skew-strain from a given
scale of motion makes no contribution to energy flux across eddies at that
scale, so that the inverse cascade cannot be strongly scale-local. We show that
this conclusion extends a result of Kraichnan for spectral transfer and is due
to absence of vortex-stretching in 2D. This `weakly local' mechanism of inverse
cascade requires a relative rotation between the principal directions of strain
at different scales and we argue for this using both the dynamical equations of
motion and also a heuristic model of `thinning' of small-scale vortices by an
imposed large-scale strain. Carrying out our expansion to second-order in
gradients, we find two additional terms in the stress that can contribute to
energy cascade. The first is a Newtonian stress with an `eddy-viscosity' due to
differential strain-rotation, and the second is a tensile stress exerted along
vorticity contour-lines. The latter was anticipated by Kraichnan for a very
special model situation of small-scale vortex wave-packets in a uniform strain
field. We prove a proportionality in 2D between the mean rates of differential
strain-rotation and of vorticity-gradient stretching, analogous to a similar
relation of Betchov for 3D. According to this result the second-order stresses
will also contribute to inverse cascade when, as is plausible, vorticity
contour-lines lengthen on average by turbulent advection.


title: Fokker - Planck equation in curvilinear coordinates. Part 2

abstract:
  The aim of this paper is to derive Fokker - Planck equation in curvilinear
coordinates using physical argumentation. We get the same result, as in our
previous article [1], but for broader class of arbitrary holonomic mechanical
systems.


title:
Self-other organization: Why early life did not evolve through natural
  selection

abstract:
  The improbability of a spontaneously generated self-assembling molecule has
suggested that life began with a set of simpler, collectively replicating
elements, such as an enclosed autocatalytic set of polymers (or protocell).
Since replication occurs without a self-assembly code, acquired characteristics
are inherited. Moreover, there is no strict distinction between alive and dead;
one can only infer that a protocell was alive if it replicates. These features
of early life render natural selection inapplicable to the description of its
change-of-state because they defy its underlying assumptions. Moreover, natural
selection describes only randomly generated novelty; it cannot describe the
emergence of form at the interface between organism and environment.
Self-organization is also inadequate because it is restricted to interactions
amongst parts; it too cannot account for context-driven change. A modified
version of selection theory or self-organization would not work because the
description of change-of-state through interaction with an incompletely
specified context has a completely different mathematical structure, i.e.
entails a non-Kolmogorovian probability model. It is proposed that the
evolution of early life is appropriately described as lineage transformation
through context-driven actualization of potential (CAP), with self-organized
change-of-state being a special case of no contextual influence, and
competitive exclusion of less fit individuals through a selection-like process
possibly (but not necessarily) playing a secondary role. It is argued that
natural selection played an important role in evolution only after genetically
mediated replication was established.


title:
Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov
  $\tau_2$-model for N=2

abstract:
  We find a representation of the row-to-row transfer matrix of the
Baxter-Bazhanov-Stroganov $\tau_2$-model for N=2 in terms of an integral over
two commuting sets of grassmann variables. Using this representation, we
explicitly calculate transfer matrix eigenvectors and normalize them. It is
also shown how form factors of the model can be expressed in terms of
determinants and inverses of certain Toeplitz matrices.


title:
Formation of fractal structure in many-body systems with attractive
  power-law potentials

abstract:
  We study the formation of fractal structure in one-dimensional many-body
systems with attractive power-law potentials. Numerical analysis shows that the
range of the index of the power for which fractal structure emerges is limited.
Dependence of the growth rate on wavenumber and power-index is obtained by
linear analysis of the collisionless Boltzmann equation, which supports the
numerical results.


title: Multi-peaked localized states of DNLS in one and two dimensions

abstract:
  Multi-peaked localized stationary solutions of the discrete nonlinear
Schrodinger (DNLS) equation are presented in one (1D) and two (2D) dimensions.
These are excited states of the discrete spectrum and correspond to
multi-breather solutions. A simple, very fast, and efficient numerical method,
suggested by Aubry, has been used for their calculation. The method involves no
diagonalization, but just iterations of a map, starting from trivial solutions
of the anti-continuous limit. Approximate analytical expressions are presented
and compared with the numerical results. The linear stability of the calculated
stationary states is discussed and the structure of the linear stability
spectrum is analytically obtained for relatively large values of nonlinearity.


title: Stabilization of ultra-short pulses in cubic nonlinear media

abstract:
  We study the propagation of ultra-short pulses in a cubic nonlinear medium.
Using multiple-scale technique, we derive a new wave equation that preserves
the nonlocal dispersion present in Maxwell's equations. As a result, we are
able to understand how ultra-short nonlinear shocks are stabilized by
dispersive terms. A delicate balance between dispersion and nonlinearity leads
to a new type of solitary waves. Their stability is confirmed by numerical
simulations of full Maxwell's equations.


title: N-Particle Dynamics of the Euler Equations for Planar Diffeomorphisms

abstract:
  The Euler equations associated with diffeomorphism groups have received much
recent study because of their links with fluid dynamics, computer vision, and
mechanics. In this paper, we consider the dynamics of $N$ point particles or
`blobs' moving under the action of the Euler equations associated with the
group of diffeomorphisms of the plane in a variety of different metrics. The 2
body problem is always integrable, and we analyze its phase portrait under
different metrics. In particular, we show that 2-body capturing orbits (in
which the distances between the particles tend to 0 as $t \to \infty$) can
occur when the kernel is sufficiently smooth and the relative initial velocity
of the particles is sufficiently large. We compute the dynamics of these
`dipoles' with respect to other test particles, and supplement the calculations
with simulations for larger $N$ that illustrate the different regimes.


title: Adaptive Synchronization of An Uncertain Complex Dynamical Network

abstract:
  This brief paper further investigates the locally and globally adaptive
synchronization of an uncertain complex dynamical network. Several network
synchronization criteria are deduced. Especially, our hypotheses and designed
adaptive controllers for network synchronization are rather simple in form. It
is very useful for future practical engineering design. Moreover, numerical
simulations are also given to show the effectiveness of our synchronization
approaches.


title: Integrable Anisotropic Evolution Equations on a Sphere

abstract:
  V.V. Sokolov's modifying symmetry approach is applied to anisotropic
evolution equations of the third order on the n-dimensional sphere. The main
result is a complete classification of such equations. Auto-B\"acklund
transformations are also found for all equations.


title: Fixed Energy R-separation for Schroedinger equation

abstract:
  We extend the classical approach of the R-separation of the Laplace equation
(as a null eigenvalue problem) to the general steady state Schroedinger
equation including cases where a scalar potential V is present and the energy
is a fixed constant.


title: Quaternions and particle dynamics in the Euler fluid equations

abstract:
  Vorticity dynamics of the three-dimensional incompressible Euler equations is
cast into a quaternionic representation governed by the Lagrangian evolution of
the tetrad consisting of the growth rate and rotation rate of the vorticity. In
turn, the Lagrangian evolution of this tetrad is governed by another that
depends on the pressure Hessian. Together these form the basis for a direction
of vorticity theorem. Moreover, in this representation, fluid particles carry
ortho-normal frames whose Lagrangian evolution in time are shown to be directly
related to the Frenet-Serret equations for a vortex line. The frame dynamics
suggest an elegant Lagrangian relation regarding the pressure Hessian tetrad.
The equations for ideal MHD are similarly considered.


title:
Algebraic Bethe ansatz for an integrable U_q[Sl(n|m)] vertex model with
  mixed representations

abstract:
  We diagonalize the transfer matrix of a solvable vertex model constructed by
combining the vector representation of U_q[Sl(n|m)] and its dual by means of
the quantum inverse scattering framework. The algebraic Bethe ansatz solution
consider all (n+m)!/(n!m!) possibilities of choosing the grading for arbitrary
values of n and m. This allows us to derive the transfer matrix eigenvalues and
the respective Bethe ansatz equations for general grading choices.


title: Partial Synchronization on Complex Networks

abstract:
  Network topology plays an important role in governing the collective
dynamics. Partial synchronization (PaS) on regular networks with a few
non-local links is explored. Different PaS patterns out of the symmetry
breaking are observed for different ways of non-local couplings. The criterion
for the emergence of PaS is studied. The emergence of PaS is related to the
loss of degeneration in Lyapunov exponent spectrum. Theoretical and numerical
analysis indicate that non-local coupling may drastically change the dynamical
feature of the network, emphasizing the important topological dependence of
collective dynamics on complex networks.


title: Transitions To the Long-Resident State in coupled chaotic oscillators

abstract:
  The behaviors of coupled chaotic oscillators before complete synchronization
were investigated. We report three phenomena: (1) The emergence of long-time
residence of trajectories besides one of the saddle foci; (2) The tendency that
orbits of the two oscillators get close becomes faster with increasing the
coupling strength; (3) The diffusion of two oscillator's phase difference is
first enhanced and then suppressed. There are exact correspondences among these
phenomena. The mechanism of these correspondences is explored. These phenomena
uncover the route to synchronization of coupled chaotic oscillators.


title:
Jump-defects in the nonlinear Schrodinger model and other
  non-relativistic field theories

abstract:
  Recent work on purely transmitting 'jump-defects' in the sine-Gordon model
and other relativistic field theories is extended to non-relativistic models.
In all the cases investigated the defect conditions are provided by 'frozen'
Backlund transformations and it is also shown via a Lax pair argument how
integrability will be preserved in the presence of this type of defect.
Explicit examples of the scattering of solitons by defects are given, and bound
states associated with 'jump-defects' in the nonlinear Schrodinger model are
described. Although the nonlinear Schrodinger model provides the principal
example, some results are also presented for the Korteweg de Vries and modified
Korteweg de Vries equations.


title: Statistical Equilibria of Uniformly Forced Advection Condensation

abstract:
  We examine the state of statistical equilibrium attained by a uniformly
forced condensable substance subjected to advection in a periodic domain. In
particular, we examine the probability density function (\pdf{}) of the
condensable substance in the limit of rapid condensation. The constraints
imposed by this limit are pointed out and are shown to result in a \pdf{} --
whenever the advecting velocity field admits a diffusive representation -- that
features a peak at small values, decays exponentially and terminates in a rapid
"roll-off" near saturation. Possible physical implications of this feature as
compared to a \pdf{} which continues to decay slowly are pointed out. A set of
simple numerical exercises which employ lattice maps for purposes of advection
are performed to test these features. Despite the simplicity of the model, the
derived \pdf{} is seen to compare favourably with \pdf{}'s constructed from
isentropic specific humidity data. Further, structure functions associated with
the condensable field are seen to scale anomalously with near saturation of the
scaling exponents for high moments -- a feature which agrees with studies of
high resolution aircraft data.

categories: nlin.PS nlin.CD physics.ao-ph physics.flu-dyn


title:
Mesa-type patterns in the one-dimensional Brusselator and their
  stability

abstract:
  The Brusselator is a generic reaction-diffusion model for a tri-molecular
chemical reaction. We consider the case when the input and output reactions are
slow. In this limit, we show the existence of $K$-periodic, spatially bi-stable
structures, \emph{mesas}, and study their stability. Using singular
perturbation techniques, we find a threshold for the stability of $K$ mesas.
This threshold occurs in the regime where the exponentially small tails of the
localized structures start to interact. By comparing our results with Turing
analysis, we show that in the generic case, a Turing instability is followed by
a slow coarsening process whereby logarithmically many mesas are annihilated
before the system reaches a steady equilibrium state. We also study a
``breather''-type instability of a mesa, which occurs due to a Hopf
bifurcation. Full numerical simulations are shown to confirm the analytical
results.


title:
Generating Function Associated with the Hankel Determinant Formula for
  the Solutions of the Painlev\'e IV Equation

abstract:
  We consider a Hankel determinant formula for generic solutions of the
Painlev\'e IV equation. We show that the generating functions for the entries
of the Hankel determinants are related to the asymptotic solution at infinity
of the isomonodromic problem. Summability of these generating functions are
also discussed.


title:
The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II
  equation revisited: recursion operators, nonlocal symmetries, and more

abstract:
  We found a new symplectic structure and a recursion operator for the
Sasa--Satsuma equation widely used in nonlinear optics, $$ p_t=p_{xxx}+6 p q
p_x+3 p (p q)_x,\quad q_t=q_{xxx}+6 p q q_x+3 q (p q)_x, $$ along with an
integro-differential substitution linking this system to a third-order
generalized symmetry of the complex sine-Gordon II system $$ u_{xy}=\frac{v u_x
u_y}{u v + c} + (2 u v + c)(u v + c) k u,\qquad v_{xy}=\frac{u v_x v_y}{u v +
c} + (2 u v + c)(u v + c) k v, $$ where $c$ and $k$ are arbitrary constants.
  Combining these two results yields a highly nonlocal hereditary recursion
operator and higher Hamiltonian structures for the complex sine-Gordon II
system. We also show that both the Sasa--Satsuma equation and the third order
evolutionary symmetry flow for the complex sine-Gordon II system are
bihamiltonian systems, and construct several hierarchies of local and nonlocal
symmetries for these systems.


title: Inverse Scattering Problem for Vector Fields and the Heavenly Equation

abstract:
  We solve the inverse scattering problem for multidimensional vector fields
and we use this result to construct the formal solution of the Cauchy problem
for the second heavenly equation of Plebanski, a scalar partial differential
equation in four dimensions relevant in General Relativity, which arises from
the commutation of multidimensional Hamiltonian vector fields


title: Generalized synchronization onset

abstract:
  The behavior of two unidirectionally coupled chaotic oscillators near the
generalized synchronization onset has been considered. The character of the
boundaries of the generalized synchronization regime has been explained by
means of the modified system


title: Synchronous Behavior of Coupled Systems with Discrete Time

abstract:
  The dynamics of one-way coupled systems with discrete time is considered. The
behavior of the coupled logistic maps is compared to the dynamics of maps
obtained using the Poincare sectioning procedure applied to the coupled
continuous-time systems in the phase synchronization regime. The behavior
(previously considered as asynchronous) of the coupled maps that appears when
the complete synchronization regime is broken as the coupling parameter
decreases, corresponds to the phase synchronization of flow systems, and should
be considered as a synchronous regime. A quantitative measure of the degree of
synchronism for the interacting systems with discrete time is proposed.


title:
Hamiltonian Flows of Curves in symmetric spaces G/SO(N) and Vector
  Soliton Equations of mKdV and Sine-Gordon Type

abstract:
  The bi-Hamiltonian structure of the two known vector generalizations of the
mKdV hierarchy of soliton equations is derived in a geometrical fashion from
flows of non-stretching curves in Riemannian symmetric spaces G/SO(N). These
spaces are exhausted by the Lie groups G=SO(N+1),SU(N). The derivation of the
bi-Hamiltonian structure uses a parallel frame and connection along the curves,
tied to a zero curvature Maurer-Cartan form on G, and this yields the vector
mKdV recursion operators in a geometric O(N-1)-invariant form. The kernel of
these recursion operators is shown to yield two hyperbolic vector
generalizations of the sine-Gordon equation. The corresponding geometric curve
flows in the hierarchies are described in an explicit form, given by wave map
equations and mKdV analogs of Schrodinger map equations.