title: Toda equation and special polynomials associated with the Garnier system

abstract:
  We prove that a certain sequence of tau functions of the Garnier system
satisfies Toda equation. We construct a class of algebraic solutions of the
system by the use of Toda equation; then show that the associated tau functions
are expressed in terms of the universal character, which is a generalization of
Schur polynomial attached to a pair of partitions.


title: Bubble generation in a twisted and bent DNA-like model

abstract:
  The DNA molecule is modeled by a parabola embedded chain with long-range
interactions between twisted base pair dipoles. A mechanism for bubble
generation is presented and investigated in two different configurations. Using
random normally distributed initial conditions to simulate thermal
fluctuations, a relationship between bubble generation, twist and curvature is
established. An analytical approach supports the numerical results.


title: Spectral statistics of a quantum interval-exchange map

abstract:
  Curious spectral properties of an ensemble of random unitary matrices
appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in
[Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer
co-prime m,n and matrix dimension N -> infinity is such that mN = 1 or -1 mod
n, local spectral statistics of this ensemble tends to the semi-Poisson
distribution [Bogomolny et al. Eur. Phys. J. B 19, 121 (2001)] with arbitrary
integer or half-integer level repulsion at small distances: R(s)-> s^{beta}
when s -> 0 and beta=n-1 or n/2-1 depending on time-reversal symmetry of the
map.


title:
Generalized Darboux Transform in the Ishimori magnet model on the
  background of spiral structures

abstract:
  The integration procedure based on the the generalized Darboux transform is
suggested for the Ishimori magnet model. Exact solutions are constructed for
the model of background of spiral structures. The possibility of phase
transition in the system is hypothesized.


title:
Solutions of the Dispersionless Toda Hierarchy Constrained by String
  Equations

abstract:
  Solutions of the Riemann-Hilbert problem implementing the twistorial
structure of the dispersionless Toda (dToda) hierarchy are obtained. Two types
of string equations are considered which characterize solutions arising in
hodograph sectors and integrable structures of two-dimensional quantum gravity
and Laplacian growth problems.


title: Variational calculation of the period of nonlinear oscillators

abstract:
  The problem of calculating the period of second order nonlinear autonomous
oscillators is formulated as an eigenvalue problem. We show that the period can
be obtained from two integral variational principles dual to each other. Upper
and lower bounds on the period can be obtained to any desired degree of
accuracy. The results are illustrated by an application to the Duffing
equation.


title: Some fractal aspects of Self-Organized Criticality

abstract:
  The concept of Self-Organized Criticality (SOC) was proposed in an attempt to
explain the widespread appearance of power-law in nature. It describes a
mechanism in which a system reaches spontaneously a state where the
characteristic events (avalanches) are distributed according to a power law. We
present a dynamical systems approach to Self-Organized Criticality where the
dynamics is described either in terms of Iterated Function Systems, or as a
piecewise hyperbolic dynamical system of skew-product type. Some results
linking the structure of the attractor and some characteristic properties of
avalanches are discussed.


title: A new criterion for the existence of KdV solitons in ferromagnets

abstract:
  The long-time evolution of the KdV-type solitons propagating in ferromagnetic
materials is considered trough a multi-time formalism, it is governed by all
equations of the KdV Hierarchy. The scaling coefficients of the higher order
time variables are explicitly computed in terms of the physical parameters,
showing that the KdV asymptotic is valid only when the angle between the
propagation direction and the external magnetic field is large enough. The
one-soliton solution of the KdV hierarchy is written down in terms of the
physical parameters. A maximum value of the soliton parameter is determined,
above which the perturbative approach is not valid. Below this value, the KdV
soliton conserves its properties during an infinite propagation time.


title: Power Law Signature in Indonesian Population

abstract:
  The paper analyzes the spreading of population in Indonesia. The spreading of
population in Indonesia is clustered in two regional terms, i.e.: kabupaten and
kotamadya. It is interestingly found that the rank in all kabupaten respect to
the population does not have fat tail properties, while in the other hand;
there exists power-law signature in kotamadya. We analyzed that this fact could
be caused by the equal or similar infrastructural development in all regions;
nevertheless, we also note that the first 20 kabupatens are dominated in Java
and Sumatera. Furthermore, the fat tail character in the rank of kotamadya
could be caused by the big gap between big cities one another, e.g.: Jakarta,
Surabaya, and others. The paper ends with some suggestions of more attention to
infrastructural development in eastern regional cities.


title: Fidelity Decay for Phase Space Displacements

abstract:
  In this letter we analyse the behavior of fidelity decay under a very
specific kind of perturbation: phase space displacements. Under these
perturbations, systems will decay following the Lyapunov regime only. Others
universal regimes discussed in the literature are not presented in this case;
instead, for small values of the perturbation we observe quantum freeze of the
fidelity. We also show that it is possible to connect this result with the
incoherent neutron scattering problem


title: Classification of KPZQ and BDP models by multiaffine analysis

abstract:
  We argue differences between the Kardar-Parisi-Zhang with Quenched disorder
(KPZQ) and the Ballistic Deposition with Power-law noise (BDP) models, using
the multiaffine analysis method. The KPZQ and the BDP models show mono-affinity
and multiaffinity, respectively. This difference results from the different
distribution types of neighbor-height differences in growth paths. Exponential
and power-law distributions are observed in the KPZQ and the BDP, respectively.
In addition, we point out the difference of profiles directly, i.e., although
the surface profiles of both models and the growth path of the BDP model are
rough, the growth path of the KPZQ model is smooth.


title:
Asymptotic behavior of small solutions for the discrete nonlinear
  Schr\"odinger and Klein-Gordon equations

abstract:
  We show decay estimates for the propagator of the discrete Schr\"odinger and
Klein-Gordon equations in the form $\norm{U(t)f}{l^\infty}\leq C
(1+|t|)^{-d/3}\norm{f}{l^1}$. This implies a corresponding (restricted) set of
Strichartz estimates. Applications of the latter include the existence of
excitation thresholds for certain regimes of the parameters and the decay of
small initial data for relevant $l^p$ norms. The analytical decay estimates are
corroborated with numerical results.


title: Localization of nonlinear excitations in curved waveguides

abstract:
  Motivated by the example of a curved waveguide embedded in a photonic
crystal, we examine the effects of geometry in a ``quantum channel'' of
parabolic form. We study the linear case and derive exact as well as
approximate expressions for the eigenvalues and eigenfunctions of the linear
problem. We then proceed to the nonlinear setting and its stationary states in
a number of limiting cases that allow for analytical treatment. The results of
our analysis are used as initial conditions in direct numerical simulations of
the nonlinear problem and localized excitations are found to persist, as well
as to have interesting relaxational dynamics. Analogies of the present problem
in contexts related to atomic physics and particularly to Bose-Einstein
condensation are discussed.


title: Resonance Patterns in a Stadium-shaped Microcavity

abstract:
  We investigate resonance patterns in a stadium-shaped microcavity around
$n_ck R \simeq 10$, where $n_c$ is the refractive index, $k$ the vacuum
wavenumber, and $R$ the radius of the circular part of the cavity. We find that
the patterns of high $Q$ resonances can be classified, even though the
classical dynamics of the stadium system is chaotic. The patterns of the high
$Q$ resonances are consistent with the ray dynamical consideration, and appears
as the stationary lasing modes with low pumping rate in the nonlinear dynamical
model. All resonance patterns are presented in a finite range of $kR$.


title:
Semiclassical form factor for spectral and matrix element fluctuations
  of multi-dimensional chaotic systems

abstract:
  We present a semiclassical calculation of the generalized form factor which
characterizes the fluctuations of matrix elements of the quantum operators in
the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on
some recently developed techniques for the spectral form factor of systems with
hyperbolic and ergodic underlying classical dynamics and f=2 degrees of
freedom, that allow us to go beyond the diagonal approximation. First we extend
these techniques to systems with f>2. Then we use these results to calculate
the generalized form factor. We show that the dependence on the rescaled time
in units of the Heisenberg time is universal for both the spectral and the
generalized form factor. Furthermore, we derive a relation between the
generalized form factor and the classical time-correlation function of the Weyl
symbols of the quantum operators.


title: Epistemic communities: description and hierarchic categorization

abstract:
  Social scientists have shown an increasing interest in understanding the
structure of knowledge communities, and particularly the organization of
"epistemic communities", that is groups of agents sharing common knowledge
concerns. However, most existing approaches are based only on either social
relationships or semantic similarity, while there has been roughly no attempt
to link social and semantic aspects. In this paper, we introduce a formal
framework addressing this issue and propose a method based on Galois lattices
(or concept lattices) for categorizing epistemic communities in an automated
and hierarchically structured fashion. Suggesting that our process allows us to
rebuild a whole community structure and taxonomy, and notably fields and
subfields gathering a certain proportion of agents, we eventually apply it to
empirical data to exhibit these alleged structural properties, and successfully
compare our results with categories spontaneously given by domain experts.


title: Dynamics of inhomogeneous one--dimensional coupled map lattices

abstract:
  We study the dynamics of one--dimensional discrete models of one--component
active medium built up of spatially inhomogeneous chains of diffusively coupled
piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms
of parameter difference in the corresponding maps. Two types of space defects
are considered: periodic and localized. We elaborate analytic approach to
obtain the regions with the qualitatively different behaviour in the parametric
space. For the model with space--periodic nonhomogeneities we found an exact
boundary separating the regions of regular and chaotic dynamics. For the chain
with a unique (localized) defect the numerical estimate is given. The effect of
the nonhomegeneity on the global dynamics of the system is analyzed.


title:
Fluctuations of a homeotropically aligned nematic liquid crystal in the
  presence of an applied voltage

abstract:
  We determined the refractive-index structure-factor $S_n(\bf k)$ from
shadowgraphs of fluctuations in a layer of a homeotropically aligned nematic
liquid crystal with negative dielectric anisotropy in the presence of an ac
voltage of amplitude $V_0$ applied orthogonal to the layer. $S_n(\bf k)$ had
rotational symmetry. Its integral $P(V_0)$ and amplitude $B(V_0)$ increased
smoothly through the Fr\'eedericksz transition at $V_0 = V_F$. Its inverse
width $\xi(V_0)$ and its relaxation rate $\Gamma_0(V_0)$ had cusps but remained
finite at $V_F$. The results are inconsistent with the critical mode at a
second-order phase transition.


title: Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

abstract:
  We present evidence that nonlinear resonances govern the tunneling process
between symmetry-related islands of regular motion in mixed regular-chaotic
systems.In a similar way as for near-integrable tunneling, such resonances
induce couplings between regular states within the islands and states that are
supported by the chaotic sea. On the basis of this mechanism, we derive a
semiclassical expression for the average tunneling rate, which yields good
agreement in comparison with the exact quantum tunneling rates calculated for
the kicked rotor and the kicked Harper.


title: Multifractals via recurrence times ?

abstract:
  This letter is a comment on an article by T.C. Halsey and M.H. Jensen in
Nature about using recurrence times as a reliable tool to estimate multifractal
dimensions of strange attractors. Our aim is to emphasize that in the recent
mathematical literature (not cited by these authors), there are positive as
well as negative results about the use of such techniques. Thus one may be
careful in using this tool in practical situations (experimental data).


title:
Universal decay of classical Loschmidt echo of neutrally stable but
  mixing dynamics

abstract:
  We provide analytical and numerical evidence that classical mixing systems
which lack exponential sensitivity on initial conditions, exhibit universal
decay of Loschmidt echo which turns out to be a function of a single scaled
time variable delta^(2/5)t, where delta is the strength of perturbation. The
role of dynamical instability and entropy production is discussed.


title: Lyapunov modes in soft-disk systems

abstract:
  Lyapunov modes are periodic spatial perturbations of phase-space states of
many-particle systems, which are associated with the small positive or negative
Lyapunov exponents. Although familiar for hard-particle systems in one, two,
and three dimensions, they have been difficult to find for soft-particles. We
present computer simulations for soft-disk systems in two dimensions and
demonstrate the existence of the modes, where also Fourier-transformation
methods are employed. We discuss some of their properties in comparison with
equivalent hard-disk results. The whole range of densities corresponding to
fluids is considered. We show that it is not possible to represent the modes by
a two-dimensional vector field of the position perturbations alone (as is the
case for hard disks), but that the momentum perturbations are simultaneously
required for their characterization.


title: New class of symmetries for self-gravitating hydrodynamics equations

abstract:
  A method of calculating a new class of symmetries is presented for partial
differential equations. The method give a new dynamical solution for an
isothermal and cylindrically symmetric hydrodynamics equations under
self-gravity. The solution describes a development of a gas cylinder from a
motion-less state to states of expansion and oscillation.


title: Fidelity recovery in chaotic systems and the Debye-Waller factor

abstract:
  Using supersymmetry calculations and random matrix simulations, we studied
the decay of the average of the fidelity amplitude f_epsilon(tau)=<psi(0)|
exp(2 pi i H_epsilon tau) exp(-2 pi i H_0 tau) |psi(0)>, where H_epsilon
differs from H_0 by a slight perturbation characterized by the parameter
epsilon. For strong perturbations a recovery of f_epsilon(tau) at the
Heisenberg time tau=1 is found. It is most pronounced for the Gaussian
symplectic ensemble, and least for the Gaussian orthogonal one. Using Dyson's
Brownian motion model for an eigenvalue crystal, the recovery is interpreted in
terms of a spectral analogue of the Debye-Waller factor known from solid state
physics, describing the decrease of X-ray and neutron diffraction peaks with
temperature due to lattice vibrations.


title:
The global picture of self-similar and not self-similar decay in Burgers
  Turbulence

abstract:
  This paper continue earlier investigations on the decay of Burgers turbulence
in one dimension from Gaussian random initial conditions of the power-law
spectral type $E_0(k)\sim|k|^n$. Depending on the power $n$, different
characteristic regions are distinguished. The main focus of this paper is to
delineate the regions in wave-number $k$ and time $t$ in which self-similarity
can (and cannot) be observed, taking into account small-$k$ and large-$k$
cutoffs. The evolution of the spectrum can be inferred using physical arguments
describing the competition between the initial spectrum and the new frequencies
generated by the dynamics. For large wavenumbers, we always have $k^{-2}$
region, associated to the shocks. When $n$ is less than one, the large-scale
part of the spectrum is preserved in time and the global evolution is
self-similar, so that scaling arguments perfectly predict the behavior in time
of the energy and of the integral scale. If $n$ is larger than two, the
spectrum tends for long times to a universal scaling form independent of the
initial conditions, with universal behavior $k^2$ at small wavenumbers. In the
interval $2<n$ the leading behaviour is self-similar, independent of $n$ and
with universal behavior $k^2$ at small wavenumber. When $1<n<2$, the spectrum
has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with
a time-independent constant, second, a $k^2$ region at intermediate
wavenumbers, finally, the usual $k^{-2}$ region. In the remaining interval,
$n<-3$ the small-$k$ cutoff dominates, and $n$ also plays no role. We find also
(numerically) the subleading term $\sim k^2$ in the evolution of the spectrum
in the interval $-3<n<1$. High-resolution numerical simulations have been
performed confirming both scaling predictions and analytical asymptotic theory.


title: Resonant light scattering by optical solitons

abstract:
  We consider the process of light scattering by optical solitons in a planar
waveguide with homogeneous and inhomogeneous refractive index core. We observe
resonant reflection (Fano resonances) as well as resonant transmission of light
by optical solitons. All resonant effects can be controlled in experiment by
changing the soliton intensity.


title: Quantifying Self-Organization with Optimal Predictors

abstract:
  Despite broad interest in self-organizing systems, there are few
quantitative, experimentally-applicable criteria for self-organization. The
existing criteria all give counter-intuitive results for important cases. In
this Letter, we propose a new criterion, namely an internally-generated
increase in the statistical complexity, the amount of information required for
optimal prediction of the system's dynamics. We precisely define this
complexity for spatially-extended dynamical systems, using the probabilistic
ideas of mutual information and minimal sufficient statistics. This leads to a
general method for predicting such systems, and a simple algorithm for
estimating statistical complexity. The results of applying this algorithm to a
class of models of excitable media (cyclic cellular automata) strongly support
our proposal.

categories: nlin.AO cond-mat.stat-mech math.ST nlin.CG physics.data-an stat.TH


title: Assessing Turbulence Strength via Lyaponuv Exponents

abstract:
  In this paper we study the link between `turbulence strength' in a flow and
the leading Lyaponuv exponent that characterize it. To this end we use two
approaches. The first, analytical, considers the truncated convection equations
in 2-dimensions with three (Lorenz model) and six components and study their
leading Lyaponuv exponent as a function of the Rayleigh number. For the second
approach we analyze fifteen time series of measurements taken by a plane flying
at constant height in the upper troposphere. For each of these time series we
estimate the leading Lyaponuv exponent which we then correlate with the
structure constant for the temperature.


title: Dendritic side-branching with anisotropic viscous fingering

abstract:
  We studied dendritic side-branching mechanism in the experiment of
anisotropic viscous fingering. We measured the time dependence of growth speed
of side-branch and the envelop of side-branches. We found that the speed of
side-branch gets to be faster than one of the stem and the growth exponent of
the speed changes at a certain time. The envelope of side-branches is
represented as Y ~ X^1.47.


title: Nonlinear Lattice Dynamics of Bose-Einstein Condensates

abstract:
  The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine
thermalization in non-metallic solids and develop ``experimental'' techniques
for studying nonlinear problems, continues to yield a wealth of results in the
theory and applications of nonlinear Hamiltonian systems with many degrees of
freedom. Inspired by the studies of this seminal model, solitary-wave dynamics
in lattice dynamical systems have proven vitally important in a diverse range
of physical problems--including energy relaxation in solids, denaturation of
the DNA double strand, self-trapping of light in arrays of optical waveguides,
and Bose-Einstein condensates (BECs) in optical lattices. BECS, in particular,
due to their widely ranging and easily manipulated dynamical apparatuses--with
one to three spatial dimensions, positive-to-negative tuning of the
nonlinearity, one to multiple components, and numerous experimentally
accessible external trapping potentials--provide one of the most fertile
grounds for the analysis of solitary waves and their interactions. In this
paper, we review recent research on BECs in the presence of deep periodic
potentials, which can be reduced to nonlinear chains in appropriate
circumstances. These reductions, in turn, exhibit many of the remarkable
nonlinear structures (including solitons, intrinsic localized modes, and
vortices) that lie at the heart of the nonlinear science research seeded by the
FPU paradigm.

categories: nlin.PS cond-mat.soft cond-mat.stat-mech math.DS nlin.CD


title:
Clustering transition in a system of particles self-consistently driven
  by a shear flow

abstract:
  We introduce a simple model of active transport for an ensemble of particles
driven by an external shear flow. Active refers to the fact that the flow of
the particles is modified by the distribution of particles itself. The model
consists in that the effective velocity of every particle is given by the
average of the external flow velocities felt by the particles located at a
distance less than a typical radius, $R$. Numerical analysis reveals the
existence of a transition to clustering depending on the parameters of the
external flow and on $R$. A continuum description in terms of the number
density of particles is derived, and a linear stability analysis of the density
equation is performed in order to characterize the transitions observed in the
model of interacting particles.


title: Flooding of regular islands by chaotic states

abstract:
  We introduce a criterion for the existence of regular states in systems with
a mixed phase space. If this condition is not fulfilled chaotic eigenstates
substantially extend into a regular island. Wave packets started in the chaotic
sea progressively flood the island. The extent of flooding by eigenstates and
wave packets increases logarithmically with the size of the chaotic sea and the
time, respectively. This new effect can be observed for island chains with just
10 islands.


title:
Isotropic third-order statistics in turbulence with helicity: the
  2/15-law

abstract:
  The so-called 2/15-law for two-point, third-order velocity statistics in
isotropic turbulence with helicity is computed for the first time from a direct
numerical simulation of the Navier-Stokes equations in a 512^3 periodic domain.
This law is a statement of helicity conservation in the inertial range,
analogous to the benchmark Kolmogorov 4/5-law for energy conservation in
high-Reynolds number turbulence. The appropriately normalized parity-breaking
statistics, when measured in an arbitrary direction in the flow, disagree with
the theoretical value of 2/15 predicted for isotropic turbulence. They are
highly anisotropic and variable and remain so over a long times. We employ a
recently developed technique to average over many directions and so recover the
statistically isotropic component of the flow. The angle-averaged statistics
achieve the 2/15 factor to within about 7% instantaneously and about 5% on
average over time. The inertial- and viscous-range behavior of the
helicity-dependent statistics and consequently the helicity flux, which appear
in the 2/15-law, are shown to be more anisotropic and intermittent than the
cor- responding energy-dependent reflection-symmetric structure functions, and
the energy flux, which appear in the 4/5-law. This suggests that the Kolmogorov
assumption of local isotropy at high Reynolds numbers needs to be modified for
the helicity-dependent statistics investigated here.


title: A Super-Integrable Discretization of the Calogero Model

abstract:
  A time-discretization that preserves the super-integrability of the Calogero
model is obtained by application of the integrable time-discretization of the
harmonic oscillator to the projection method for the Calogero model with
continuous time. In particular, the difference equations of motion, which
provide an explicit scheme for time-integration, are explicitly presented for
the two-body case. Numerical results exhibit that the scheme conserves all
the$(=3)$ conserved quantities of the (two-body) Calogero model with a
precision of the machine epsilon times the number of iterations.


title:
Quantum integrable multi atom matter-radiation models with and without
  rotating wave approximation

abstract:
  New integrable multi-atom matter-radiation models with and without rotating
wave approximation (RWA) are constructed and exactly solved through algebraic
Bethe ansatz. The models with RWA are generated through ancestor model approach
in an unified way. The rational case yields the standard type of
matter-radiaton models, while the trigonometric case corresponds to their
q-deformations. The models without RWA are obtained from the elliptic case at
the Gaudin and high spin limit.


title: Species Abundance Patterns in Complex Evolutionary Dynamics

abstract:
  An analytic theory of species abundance patterns (SAPs) in biological
networks is presented. The theory is based on multispecies replicator dynamics
equivalent to the Lotka-Volterra equation, with diverse interspecies
interactions. Various SAPs observed in nature are derived from a single
parameter. The abundance distribution is formed like a widely observed
left-skewed lognormal distribution. As the model has a general form, the result
can be applied to similar patterns in other complex biological networks, e.g.
gene expression.


title: The short pulse equation is integrable

abstract:
  We prove that the Schafer-Wayne short pulse equation (SPE) which describes
the propagation of ultra-short optical pulses in nonlinear media is integrable.
First, we discover a Lax pair of the SPE which turns out to be of the
Wadati-Konno-Ichikawa type. Second, we construct a chain of transformations
which relates the SPE with the sine-Gordon equation.

categories: nlin.SI math-ph math.AP math.MP physics.optics


title: GridWiseTM: The Benefits of a Transformed Energy System

abstract:
  The demand for electricity is expected to continue its historical growth
trend far into the future and particularly over the 20-year projection period
discussed in this report. To meet this growth with traditional approaches will
require added generation, transmission, and distribution, costing up to $1.4
billion/GW ($1,400/kW in year 2000 dollars) on the utility side of the meter.
The amount of capacity needed in each of these categories must supply peak
demand and provide a reserve margin to protect against outages and other
contingencies. The nameplate capacity of many power system components is
typically utilized for only a few hundred hours per year. Thus, traditional
approaches to maintaining the adequacy of the nation's power generation and
delivery system are characterized by lower than desirable asset utilization,
particularly for assets located near the end-user.


title:
Estimation of the WECC System Inertia Using Observed Frequency
  Transients

abstract:
  Computer models being developed to understand the interaction between
demand-response technology, power system deregulation and market transformation
depend in part on understanding the relationship between system frequency and
load-control. Frequency, load, and plant outage events data collected over the
last several years have permitted analysis to determine the Western Electricity
Coordination Council (WECC) system's inertia during each event. This data was
used to evaluate the relationship of system inertia to total load, which is
used to model system response to load curtailment programs in next generation
power system simulations.


title:
The Equilibrium Dynamics of Thermostatic End-use Load Diversity as a
  Function of Demand

abstract:
  A recently developed state-of-the-art agent-based simulation of power
distribution systems is capable of modeling the thermal and demand response
behavior of many thousands of thermostatic end-use loads. It computes the total
power consumed by electric power customers when responding to real-time prices.
Investigation of the initialization transients has led to a more precise
understanding of the relationship between the end-use state probability of
thermostatic loads, end-use demand, and load diversity.


title:
Modeling Uncertainties in Aggregated Thermostatically Controlled Loads
  Using a State Queueing Model

abstract:
  To study the impacts of price responsive demand on the electric power system
requires better load models. This paper discusses the modeling of uncertainties
in aggregated thermostatically controlled loads using a state queueing (SQ)
model. The cycling times of thermostatically controlled appliances (TCAs) vary
with the TCA types and sizes, as well as the ambient temperatures. The random
consumption of consumers, which shortens or prolongs a specific TCA cycling
period, introduces another degree of uncertainty. By modifying the state
transition matrix, these random factors can be taken into account in a discrete
SQ model. The impacts of considering load diversity in the SQ model while
simulating TCA setpoint response are also studied.


title: Magic number 7 $\pm$ 2 in networks of threshold dynamics

abstract:
  Information processing by random feed-forward networks consisting of units
with sigmoidal input-output response is studied by focusing on the dependence
of its outputs on the number of parallel paths M. It is found that the system
leads to a combination of on/off outputs when $M \lesssim 7$, while for $M
\gtrsim 7$, chaotic dynamics arises, resulting in a continuous distribution of
outputs. This universality of the critical number $M \sim 7$ is explained by
combinatorial explosion, i.e., dominance of factorial over exponential
increase. Relevance of the result to the psychological magic number $7 \pm 2$
is briefly discussed.


title:
Hasimoto Transformation and Vortex Soliton Motion Driven by Fluid
  Helicity

abstract:
  Vorticity filament motions with respect to the Dirac bracket of Rasetti and
Regge [1975] are known to be related to the nonlinear Schr\"odinger equation by
the Hasimoto transformation (HT), when the Hamiltonian is the Local Induction
Approximation (LIA) of the kinetic energy. We show that when the Hamiltonian is
the LIA of Euler-fluid helicity $\int\mathbf{u}\cdot {\rm curl} \mathbf{u}$,
the vorticity filament equation of motion under the Rasetti-Regge Dirac bracket
is mapped by HT to the integrable complex modified Korteweg-de Vries (cmKdV)
equation, the second equation in the nonlinear Schr\"odinger hierarchy.


title: Measuring Topological Chaos

abstract:
  The orbits of fluid particles in two dimensions effectively act as
topological obstacles to material lines. A spacetime plot of the orbits of such
particles can be regarded as a braid whose properties reflect the underlying
dynamics. For a chaotic flow, the braid generated by the motion of three or
more fluid particles is computed. A ``braiding exponent'' is then defined to
characterize the complexity of the braid. This exponent is proportional to the
usual Lyapunov exponent of the flow, associated with separation of nearby
trajectories. Measuring chaos in this manner has several advantages, especially
from the experimental viewpoint, since neither nearby trajectories nor
derivatives of the velocity field are needed.


title:
Two-dimensional solitons with hidden and explicit vorticity in bimodal
  cubic-quintic media

abstract:
  We demonstrate that two-dimensional two-component bright solitons of an
annular shape, carrying vorticities $(m,\pm m)$ in the components, may be
stable in media with the cubic-quintic nonlinearity, including the
\textit{hidden-vorticity} (HV) solitons of the type $(m,-m)$, whose net
vorticity is zero. Stability regions for the vortices of both $(m,\pm m)$ types
are identified for $m=1$, 2, and 3, by dint of the calculation of stability
eigenvalues, and in direct simulations. A novel feature found in the study of
the HV solitons is that their stability intervals never reach the (cutoff)
point at which the bright vortex carries over into a dark one, hence dark HV
solitons can never be stable, contrarily to the bright ones. In addition to the
well-known symmetry-breaking (\textit{external}) instability, which splits the
ring soliton into a set of fragments flying away in tangential directions, we
report two new scenarios of the development of weak instabilities specific to
the HV solitons. One features \textit{charge flipping}, with the two components
exchanging the angular momentum and periodically reversing the sign of their
spins. The composite soliton does not split in this case, therefore we identify
such instability as an \textit{intrinsic} one. Eventually, the soliton splits,
as weak radiation loss drives it across the border of the ordinary strong
(external) instability. Another scenario proceeds through separation of the
vortex cores in the two components, each individual core moving toward the
outer edge of the annular soliton. After expulsion of the cores, there remains
a zero-vorticity breather with persistent internal vibrations.


title: Global Analysis of Synchronization in Coupled Maps

abstract:
  We introduce a new method for determining the global stability of
synchronization in systems of coupled identical maps. The method is based on
the study of invariant measures. Besides the simplest non-trivial example,
namely two symmetrically coupled tent maps, we also treat the case of two
asymmetrically coupled tent maps as well as a globally coupled network. Our
main result is the identification of the precise value of the coupling
parameter where the synchronizing and desynchronizing transitions take place.


title:
Dynamics of fluctuations below a stationary bifurcation to
  electroconvection in the planar nematic liquid crystal N4

abstract:
  We fitted $C({\bf k},\tau,\epsilon) \propto exp[-\sigma({\bf
k},\epsilon)\tau]$ to time-correlation functions $C({\bf k},\tau,\epsilon)$ of
structure factors $S({\bf k}, t, \epsilon)$ of shadowgraph images of
fluctuations below a supercritical bifurcation at $V_0 = V_c$ to
electro-convection of a planar nematic liquid crystal in the presence of a
voltage $V = \sqrt{2}V_0 cos(2\pi f t) $[${\bf k}= (p,q)$ is the wave vector
and $\epsilon \equiv V_0^2/V_{c}^2 - 1$]. There were stationary oblique
(normal) rolls at small (large) $f$. Fits of a modified Swift-Hohenberg form to
$\sigma({\bf k},\epsilon)$ gave $f$-dependent critical behavior for the minimum
decay rates $\sigma_0(\epsilon)$ and the correlations lengths
$\xi_{p,q}(\epsilon)


title: Nodal solitons and the nonlinear breaking of discrete symmetry

abstract:
  We present a new type of soliton solutions in nonlinear photonic systems with
discrete point-symmetry. These solitons have their origin in a novel mechanism
of breaking of discrete symmetry by the presence of nonlinearities. These
so-called nodal solitons are characterized by nodal lines determined by the
discrete symmetry of the system. Our physical realization of such a system is a
2D nonlinear photonic crystal fiber owning C6v symmetry.


title:
Type I intermittency in a dynamical system with dichotomous parameter
  change

abstract:
  In type I intermittency, simple models known for at least twenty years show
that a characteristic u-shaped probability distribution is obtained for the
laminar phase length. We have shown elsewhere that, for some cases of
pathology, the laminar phase length distribution characteristic for type I
intermittency may be obtained in human heart rate variability data. The heart
and its regulatory systems are presumed to be both noisy and nonstationary.
Although the effect of additive noise on the laminar phase distribution in type
I intermittency is well known, neither the effect of multiplicative noise nor
of nonstationarity (i.e. changes of the control parameter with the time) have
been studied. In this paper, we first discuss the properties of two classes of
models of type I intermittency: a) the control parameter of the logistic map is
changed dichotomously from a value within the intermittency range to just below
the bifurcation point and back; b) the control parameter is changed randomly
within the same parameter range as in the model class a). We show that the
properties of both models are importantly different from those obtained for
type I intermittency in the presence additive noise as obtained by Hirsch
twenty years ago. The two models help explain some of the features seen in the
intermittency in human heart rate variability.


title:
Enhanced tracer transport by the spiral defect chaos state of a
  convecting fluid

abstract:
  To understand how spatiotemporal chaos may modify material transport, we use
direct numerical simulations of the three-dimensional Boussinesq equations and
of an advection-diffusion equation to study the transport of a passive tracer
by the spiral defect chaos state of a convecting fluid. The simulations show
that the transport is diffusive and is enhanced by the spatiotemporal chaos.
The enhancement in tracer diffusivity follows two regimes. For large Peclet
numbers (that is, small molecular diffusivities of the tracer), we find that
the enhancement is proportional to the Peclet number. For small Peclet numbers,
the enhancement is proportional to the square root of the Peclet number. We
explain the presence of these two regimes in terms of how the local transport
depends on the local wave numbers of the convection rolls. For large Peclet
numbers, we further find that defects cause the tracer diffusivity to be
enhanced locally in the direction orthogonal to the local wave vector but
suppressed in the direction of the local wave vector.


title:
Statistics of noise-driven coupled nonlinear oscillators: applications
  to systems with Kerr nonlinearity

abstract:
  We present exact analytical results for the statistics of nonlinear coupled
oscillators under the influence of additive white noise. We suggest a
perturbative approach for analysing the statistics of such systems under the
action of a deterministic perturbation, based on the exact expressions for
probability density functions for noise-driven oscillators. Using our
perturbation technique we show that our results can be applied to studying the
optical signal propagation in noisy fibres at (nearly) zero dispersion as well
as to weakly nonlinear lattice models with additive noise. The approach
proposed can account for a wide spectrum of physically meaningful perturbations
and is applicable to the case of large noise strength.


title: The Anti-FPU Problem

abstract:
  We present a detailed analysis of the modulational instability of the
zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU)
lattices. Following this instability, a process of relaxation to equipartition
takes place, which we have called the Anti-FPU problem because the energy is
initially fed into the highest frequency part of the spectrum, at variance with
the original FPU problem (low frequency excitations of the lattice). This
process leads to the formation of chaotic breathers in both one and two
dimensions. Finally, the system relaxes to energy equipartition on time scales
which increase as the energy density is decreased. We show that breathers
formed when cooling the lattice at the edges, starting from a random initial
state, bear strong qualitative similarities with chaotic breathers.


title: An integrable generalization of the Toda law to the square lattice

abstract:
  We generalize the Toda lattice (or Toda chain) equation to the square
lattice; i.e., we construct an integrable nonlinear equation, for a scalar
field taking values on the square lattice and depending on a continuous (time)
variable, characterized by an exponential law of interaction in both discrete
directions of the square lattice. We construct the Darboux-Backlund
transformations for such lattice, and the corresponding formulas describing
their superposition. We finally use these Darboux-Backlund transformations to
generate examples of explicit solutions of exponential and rational type. The
exponential solutions describe the evolution of one and two smooth
two-dimensional shock waves on the square lattice.

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


title:
Integrability of $n$-dimensional dynamical systems of type $E_7^{(1)}$
  and $E_8^{(1)}$

abstract:
  We propose an $n$-dimensional analogue of elliptic difference Painlev\'e
equation. Some Weyl group acts on a family of rational varieties obtained by
successive blow-ups at $m$ points in $\mpp^n(\mc)$, and in many cases they
include the affine Weyl groups with symmetric Cartan matrices as subgroups. It
is shown that the dynamical systems obtained by translations of these affine
Weyl groups possess commuting flows and that their degrees grow quadratically.
For the $E_7^{(1)}$ and $E_8^{(1)}$ cases, existence of preserved quantities is
investigated. The elliptic difference case is also studied.


title:
Periodic travelling waves in the theta model for synaptically connected
  neurons

abstract:
  We study periodic travelling waves in the Theta model for a linear continuum
of synaptically-interacting neurons. We prove that when the neurons are
oscillatory, at least one periodic travelling of every wave number always
exists. In the case of excitable neurons, we prove that no periodic travelling
waves exist when the synaptic coupling is weak, and at least two periodic
travelling waves of each wave-number, a `fast' one and a `slow' one, exist when
the synaptic coupling is sufficiently strong. We derive explicit upper and
lower bounds for the `critical' coupling strength as well as for the wave
velocities. We also study the limits of large wave-number and of small
wave-number, in which results which are independent of the form of the
synaptic-coupling kernel can be obtained. Results of numerical computations of
the periodic travelling waves are also presented.


title:
Chaos Beyond Linearized Stability Analysis: Folding of the Phase Space
  and Distribution of Lyapunov Exponents

abstract:
  We consider a mechanism for area preserving Hamiltonian systems which leads
to the enhanced probability, $P(\lambda, t)$, to find small values of the
finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic
dynamical systems we go beyond the linearized stability analysis of nearby
divergent trajectories and consider folding of the phase space in the course of
chaotic evolution. We show that the spectrum of the Lyapunov exponents
$F(\lambda)= \lim_{t\to\infty} t^{-1}\ln P(\lambda, t)$ at the origin has a
finite value $F(0)=-\tilde{\lambda}$ and a slope $F'(0)\le 1$. This means that
all negative moments of the distribution $<e^{-m\lambda t}>$ are saturated by
rare events with $\lambda\to 0$. Extensive numerical simulations confirm our
findings.


title: Hierarchy of piecewise non-linear maps with non-ergodicity behavior

abstract:
  We study the dynamics of hierarchy of piecewise maps generated by
one-parameter families of trigonometric chaotic maps and one-parameter families
of elliptic chaotic maps of $\mathbf{cn}$ and $\mathbf{sn}$ types, in detail.
We calculate the Lyapunov exponent and Kolmogorov-Sinai entropy of the these
maps with respect to control parameter. Non-ergodicity of these piecewise maps
is proven analytically and investigated numerically . The invariant measure of
these maps which are not equal to one or zero, appears to be characteristic of
non-ergodicity behavior. A quantity of interest is the Kolmogorov-Sinai
entropy, where for these maps are smaller than the sum of positive Lyapunov
exponents and it confirms the non-ergodicity of the maps.


title: Phase-space correlations of chaotic eigenstates

abstract:
  It is shown that the Husimi representations of chaotic eigenstates are
strongly correlated along classical trajectories. These correlations extend
across the whole system size and, unlike the corresponding eigenfunction
correlations in configuration space, they persist in the semiclassical limit. A
quantitative theory is developed on the basis of Gaussian wavepacket dynamics
and random-matrix arguments. The role of symmetries is discussed for the
example of time-reversal invariance.


title:
Combination of anticipated and isochronous synchronization in coupled
  semiconductor lasers system

abstract:
  Combination of two basic types of synchronization, anticipated and
isochronous synchronization, is investigated numerically in coupled
semiconductor lasers. Due to the combination, a synchronization of good quality
can be obtained. We study the dependence of the lag time between two lasers and
the synchronization quality on the converse coupling retardation time
$\tau_{c21}$. When $\tau_{c21}$ is close to the difference of external cavity
round trip time $\tau$ and coupling retardation time $\tau_{c12}$, the
combination of anticipated and isochronous synchronization may produce a better
synchronization, with a lag time proportional to $\tau_{c21}$. When
$\tau_{c21}$ is largely different from $\tau-\tau_{c12}$, the combination is
noneffective and even negative in some cases, with a lag time independent of
$\tau_{c21}$.


title: Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

abstract:
  Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable
nonlinearity are reported. For finite lattices we find two different
standing-wave-like solutions, and for an infinite lattice we find a localized
soliton-like solution. The existence requirements and stability of these
solutions are discussed, and we find that our solutions are linearly stable in
most cases. We also show that the effective Peierls-Nabarro barrier potential
is nonzero thereby indicating that this discrete model is quite likely
nonintegrable.


title:
Exact theory of localized and periodic structures in active optical
  cavity

abstract:
  The nonlocal order parameter equation for nonlinear optical resonator is
approximated in the limit of high Fresnel number by the Swift- Hohenberg
equation. The exact soliton and periodic solutions of the Swift- Hohenberg
equation for optical resonator with thin slice gain element are obtained. It is
shown that hyperbolic "flat" secant, "chirped" secant and Jacobi elliptic
functions solutions in one transverse dimension are nonlinear eigenmodes for
plane - parallel, confocal and quasiconfocal geometries.


title: Dynamic Domains Networks

abstract:
  We present a model for the description of the evolution of contacts among
individuals in a network. At each time step each individual is associated with
a domain or neighborhood of fully connected agents.The dynamics of this
changing neighborhood will later be translated into a situation where the links
between individuals are also dynamic. A characterization in terms of the
parameters that govern the evolution of the network and a comparison to
previous work on Small World networks is presented as well.


title:
Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly
  oscillating dispersion coefficient

abstract:
  Using the numerical solution of the nonlinear Schroedinger equation and a
variational method it is shown that (3+1)-dimensional spatiotemporal optical
solitons can be stabilized by a rapidly oscillating dispersion coefficient in a
Kerr medium with cubic nonlinearity. This has immediate consequence in
generating dispersion-managed robust optical soliton in communication as well
as possible stabilized Bose-Einstein condensates in periodic optical-lattice
potential via an effective-mass formulation. We also critically compare the
present stabilization with that obtained by a rapid sinusoidal oscillation of
the Kerr nonlinearity parameter.


title: On Hamiltonian flows on Euler-type equations

abstract:
  Properties of Hamiltonian symmetry flows on hyperbolic Euler-type Liouvillean
equations E' are analyzed. Description of their Noether symmetries assigned to
the integrals for these equations is obtained. The integrals provide Miura
transformations from E' to the multi-component wave equations E. By using these
substitutions, we generate an infinite-Hamiltonian commutative subalgebra A of
local Noether symmetry flows on E proliferated by weakly nonlocal recursion
operators. We demonstrate that the correlation between the Magri schemes for A
and for the induced "modified" Hamiltonian flows B in the symmetry algebra of
E' is such that these properties are transferred to B and the recursions for E'
are factorized. Two examples associated with the 2D Toda lattice are
considered.


title:
Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf
  equation

abstract:
  Recently, a new model of propagation of the light through the so-called
weakly three-dimensional Cole-Cole nonlinear medium with short-range
nonlocality has been proposed. In particular, it has been shown that in the
geometrical optics limit, the model is integrable and it is governed by the
dispersionless Veselov-Novikov (dVN) equation.
  Burgers-Hopf equation can be obtained as 1+1-dimensional reduction of dVN
equation. We discuss its properties in the specific context of nonlinear
geometrical optics. An illustrative explicit example is considered.


title: Integrable Deformations of Algebraic Curves

abstract:
  A general scheme for determining and studying integrable deformations of
algebraic curves, based on the use of Lenard relations, is presented. We
emphasize the use of several types of dynamical variables : branches, power
sums and potentials.


title:
Deterministic Bak-Sneppen model. Lyapunov spectrum and avalanches as
  return times

abstract:
  A deterministic version of the Bak-Sneppen model is studied. The role of the
Lyapunov spectrum in the onset of scale-free behavior is established and
avalanches are interpreted as return times to a zero-measure set. The problem
of accurate determination of the scaling exponents near the critical barrier is
addressed using a characteristic function approach. A general equation for
return times to a small measure set is established and used to obtain
information on the nature of Bak-Sneppen dynamics.


title: Some incidence theorems and integrable discrete equations

abstract:
  Several incidence theorems of planar projective geometry are considered. It
is demonstrated that generalizations of Pascal theorem due to M\"obius give
rise to double cross-ratio equation and Hietarinta equation. The construction
corresponding to the double cross-ratio equation is a reduction to a conic
section of some planar configuration $(20_3 15_4)$. This configuration provides
a correct definition of the multidimensional quadrilateral lattices on the
plane.


title:
Standing Waves in a Non-linear 1D Lattice : Floquet Multipliers, Krein
  Signatures, and Stability

abstract:
  We construct a class of exact commensurate and incommensurate standing wave
(SW) solutions in a piecewise smooth analogue of the discrete non-linear
Schr\"{o}dinger (DNLS) model and present their linear stability analysis. In
the case of the commensurate SW solutions the analysis reduces to the
eigenvalue problem of a transfer matrix depending parametrically on the
eigenfrequency. The spectrum of eigenfrequencies and the corresponding
eigenmodes can thereby be determined exactly. The spatial periodicity of a
commensurate SW implies that the eigenmodes are of the Bloch form,
characterised by an even number of Floquet multipliers. The spectrum is made up
of bands that, in general, include a number of transition points corresponding
to changes in the disposition of the Floquet multipliers. The latter
characterise the different band segments. An alternative characterisation of
the segments is in terms of the Krein signatures associated with the
eigenfrequencies. When one or more parameters characterising the SW solution is
made to vary, one occasionally encounters collisions between the band-edges or
the intra-band transition points and, depending on the the Krein signatures of
the colliding bands or segments, the spectrum may stretch out in the complex
plane, leading to the onset of instability. We elucidate the correlation
between the disposition of Floquet multipliers and the Krein signatures,
presenting two specific examples where the SW possesses a definite window of
stability, as distinct from the SW's obtained close to the anticontinuous and
linear limits of the DNLS model.


title: Line Structures in Recurrence Plots

abstract:
  Recurrence plots exhibit line structures which represent typical behaviour of
the investigated system. The local slope of these line structures is connected
with a specific transformation of the time scales of different segments of the
phase-space trajectory. This provides us a better understanding of the
structures occuring in recurrence plots. The relationship between the
time-scales and line structures are of practical importance in cross recurrence
plots. Using this relationship within cross recurrence plots, the time-scales
of differently sampled or time-transformed measurements can be adjusted. An
application to geophysical measurements illustrates the capability of this
method for the adjustment of time-scales in different measurements.

categories: nlin.CD math-ph math.MP physics.data-an physics.geo-ph


title: Functional representation of the Volterra hierarchy

abstract:
  In this paper I study the functional representation of the Volterra hierarchy
(VH). Using the Miwa's shifts I rewrite the infinite set of Volterra equations
as one functional equation. This result is used to derive a formal solution of
the associated linear problem, a generating function for the conservation laws
and to obtain a new form of the Miura and Backlund transformations. I also
discuss some relations between the VH and KP hierarchy.


title:
Bistable analytic-phase synchronization in strongly-competing chaotic
  lasing modes

abstract:
  We theoretically study analytic-phase synchronization in strongly-competing
oscillator systems. Using the example of composite-cavity modes coupled via a
class-B laser active medium, we discover that inherent chaotic phase
synchronization can arise concurrently at two different chaotic attractors,
leading to bistable phase-synchronized solutions. In our example, the
underlying mechanism for bistability and inherent phase synchronization is
population pulsation within the active medium.


title: Nonlinear Schr\"{o}dinger lattices I: Stability of discrete solitons

abstract:
  We consider the discrete solitons bifurcating from the anti-continuum limit
of the discrete nonlinear Schr\"{o}dinger (NLS) lattice. The discrete soliton
in the anti-continuum limit represents an arbitrary finite superposition of
{\em in-phase} or {\em anti-phase} excited nodes, separated by an arbitrary
sequence of empty nodes. By using stability analysis, we prove that the
discrete solitons are all unstable near the anti-continuum limit, except for
the solitons, which consist of alternating anti-phase excited nodes. We
classify analytically and confirm numerically the number of unstable
eigenvalues associated with each family of the discrete solitons.


title:
Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha
  equations

abstract:
  We examine the effects of turbulence on elliptic instability of rotating
stratified incompressible flows, in the context of the Lagragian-averaged
Euler-Boussinesq-alpha, or \laeba, model of turbulence. We find that the \laeba
model alters the instability in a variety of ways for fixed Rossby number and
Brunt-V\"ais\"al\"a frequency. First, it alters the location of the instability
domains in the $(\gamma,\cos\theta)-$parameter plane, where $\theta$ is the
angle of incidence the Kelvin wave makes with the axis of rotation and $\gamma$
is the eccentricity of the elliptic flow, as well as the size of the associated
Lyapunov exponent. Second, the model shrinks the width of one instability band
while simultaneously increasing another. Third, the model introduces bands of
unstable eccentric flows when the Kelvin wave is two-dimensional. We introduce
two similarity variables--one is a ratio of the Brunt-V\"ais\"al\"a frequency
to the model parameter $\Upsilon_0 = 1+\alpha^2\beta^2$, and the other is the
ratio of the adjusted inverse Rossby number to the same model parameter. Here,
$\alpha$ is the turbulence correlation length, and $\beta$ is the Kelvin wave
number. We show that by adjusting the Rossby number and Brunt-V\"ais\"al\"a
frequency so that the similarity variables remain constant for a given value of
$\Upsilon_0$, turbulence has little effect on elliptic instability for small
eccentricities $(\gamma \ll 1)$. For moderate and large eccentricities,
however, we see drastic changes of the unstable Arnold tongues due to the
\laeba model.


title: Shear effects on passive scalar spectra

abstract:
  The effects of a large-scale shear on the energy spectrum of a passively
advected scalar field are investigated. The shear is superimposed on a
turbulent isotropic flow, yielding an Obukhov-Corrsin $k^{-5/3}$ scalar
spectrum at small scales. Shear effects appear at large scales, where a
different, anisotropic behavior is observed. The scalar spectrum is shown to
behave as $k^{-4/3}$ for a shear fixed in intensity and direction. For other
types of shear characteristics, the slope is generally intermediate between the
-5/3 Obukhov-Corrsin's and the -1 Batchelor's values. The physical mechanisms
at the origin of this behaviour are illustrated in terms of the motion of
Lagrangian particles. They provide an explanation to the scalar spectra shallow
and dependent on the experimental conditions observed in shear flows at
moderate Reynolds numbers.


title:
Investigation of Quantum Chaos in the Parametric Dependent System of
  Interacting oscillators

abstract:
  Formation of chaos in the parametric dependent system of interacting
oscillators for the both classical and quantum cases has been investigated.
Domain in which classical motion is chaotic is defined. It has been shown that
for certain values of the parameters from this domain, form of the classical
power spectrum is in a good agreement with the quantum band profile. Local
density of states is calculated. The range in which application of perturbation
theory is correct has been defined.


title: Quantum chaos at the Kinetic Stage of Evolution

abstract:
  It is shown that a periodic perturbation of the quantum pendulum (similarly
to the classical one) in the neighbourhood of the separatrix can bring about
irreversible phenomena. As a result of recurrent passages between degenerate
states, the system gets self-chaotized and passes from the pure state to the
mixed one. Chaotization involves the states, the branch points of whose levels
participate in a slow "drift" of the system along the Mathieu characteristics
this "drift" being caused by a slowly changing variable field. Recurrent
relations are obtained for populations of levels participating in the
irreversible evolution process. It is shown that the entropy of the system
first grows and, after reaching the equilibrium state, acquires a constant
value.


title:
Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Benard
  turbulence

abstract:
  The Rayleigh (Ra) and Prandtl (Pr) number scaling of the Nusselt number Nu,
the Reynolds number Re, the temperature fluctuations, and the kinetic and
thermal dissipation rates is studied for (numerical) homogeneous
Rayleigh-Benard turbulence, i.e., Rayleigh-Benard turbulence with periodic
boundary conditions in all directions and a volume forcing of the temperature
field by a mean gradient. This system serves as model system for the bulk of
Rayleigh-Benard flow and therefore as model for the so called ``ultimate regime
of thermal convection''. With respect to the Ra dependence of Nu and Re we
confirm our earlier results \cite{loh03} which are consistent with the
Kraichnan theory \cite{kra62} and the Grossmann-Lohse (GL) theory
\cite{gro00,gro01,gro02,gro04}, which both predict $Nu \sim Ra^{1/2}$ and $Re
\sim Ra^{1/2}$. However the Pr dependence within these two theories is
different. Here we show that the numerical data are consistent with the GL
theory $Nu \sim Pr^{1/2}$, $Re \sim Pr^{-1/2}$. For the thermal and kinetic
dissipation rates we find $\eps_\theta/(\kappa \Delta^{2}L^{-2}) \sim (Re
Pr)^{0.87}$ and $\eps_u/(\nu^3 L^{-4}) \sim Re^{2.77}$, also both consistent
with the GL theory, whereas the temperature fluctuations do not depend on Ra
and Pr. Finally, the dynamics of the heat transport is studied and put into the
context of a recent theoretical finding by Doering et al. \cite{doe05}.


title: Gap solitons in a model of a hollow optical fiber

abstract:
  We introduce a models for two coupled waves propagating in a hollow-core
fiber: a linear dispersionless core mode, and a dispersive nonlinear
quasi-surface one. The linear coupling between them may open a bandgap, through
the mechanism of the avoidance of crossing between dispersion curves. The
third-order dispersion of the quasi-surface mode is necessary for the existence
of the gap. Numerical investigation reveals that the entire bandgap is filled
with solitons, and they all are stable in direct simulations. The gap-soliton
(GS) family is extended to include pulses moving relative to the given
reference frame, up to limit values of the corresponding boost $\delta $,
beyond which the solitons do not exists. The limit values are nonsymmetric for
$\delta >0$ and $\delta <0$. The extended gap is also entirely filled with the
GSs, all of which are stable in simulations. Recently observed solitons in
hollow-core photonic-crystal fibers may belong to this GS family.


title: Nodal two-dimensional solitons in nonlinear parametric resonance

abstract:
  The parametrically driven damped nonlinear Schr\"odinger equation serves as
an amplitude equation for a variety of resonantly forced oscillatory systems on
the plane. In this note, we consider its nodal soliton solutions. We show that
although the nodal solitons are stable against radially-symmetric perturbations
for sufficiently large damping coefficients, they are always unstable to
azimuthal perturbations. The corresponding break-up scenarios are studied using
direct numerical simulations. Typically, the nodal solutions break into
symmetric "necklaces" of stable nodeless solitons.


title: Universality of Calogero-Moser model

abstract:
  In this review we explain interrelations between the Elliptic Calogero-Moser
model, integrable Elliptic Euler-Arnold top, monodromy preserving equations and
the Knizhnik-Zamolodchikov-Bernard equation on a torus.


title:
On a family of integrable systems on $S^2$ with a cubic integral of
  motion

abstract:
  We discuss a family of integrable systems on the sphere $S^2$ with an
additional integral of third order in momenta. This family contains the
Coryachev-Chaplygin top, the Goryachev system, the system recently discovered
by Dullin and Matveev and two new integrable systems. On the non-physical
sphere with zero radius all these systems are isomorphic to each other.


title:
Delocalized and Resonant Quantum Transport in Nonlinear Generalizations
  of the Kicked Rotor Model

abstract:
  We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked
Rotor. We consider two different models, in which the nonlinear term acts
either in the position or in the momentum representation. We numerically
investigate the modifications induced by the nonlinearity in the quantum
transport in both localized and resonant regimes and a comparison between the
results for the two models is presented. Analyzing the momentum distributions
and the increase of the mean square momentum, we find that the quantum
resonances asymptotically are very stable with respect to the nonlinear
perturbation of the rotor's phase evolution. For an intermittent time regime,
the nonlinearity even enhances the resonant quantum transport, leading to
superballistic motion.


title: Algebraic extensions of Gaudin models

abstract:
  We perform a In\"on\"u--Wigner contraction on Gaudin models, showing how the
integrability property is preserved by this algebraic procedure. Starting from
Gaudin models we obtain new integrable chains, that we call Lagrange chains,
associated to the same linear $r$-matrix structure. We give a general
construction involving rational, trigonometric and elliptic solutions of the
classical Yang-Baxter equation. Two particular examples are explicitly
considered: the rational Lagrange chain and the trigonometric one. In both
cases local variables of the models are the generators of the direct sum of $N$
$\mathfrak{e}(3)$ interacting tops.


title:
Pattern Formation by Boundary Forcing in Convectively Unstable,
  Oscillatory Media With and Without Differential Transport

abstract:
  Motivated by recent experiments and models of biological segmentation, we
analyze the exicitation of pattern-forming instabilities of convectively
unstable reaction-diffusion-advection (RDA) systems, occuring by means of
constant or periodic forcing at the upstream boundary. Such boundary-controlled
pattern selection is a generalization of the flow-distributed oscillation (FDO)
mechanism that can include Turing or differential flow instability (DIFI)
modes. Our goal is to clarify the relationships among these mechanisms in the
general case where there is differential flow as well as differential
diffusion. We do so by analyzing the dispersion relation for linear
perturbations and showing how its solutions are affected by differential
transport. We find a close relationship between DIFI and FDO, while the Turing
mechanism gives rise to a distinct set of unstable modes. Finally, we
illustrate the relevance of the dispersion relations using nonlinear
simulations and we discuss the experimental implications of our results.


title: Mode-Locking of mobile discrete breathers

abstract:
  We study numerically synchronization phenomena of mobile discrete breathers
in dissipative nonlinear lattices periodically forced. When varying the driving
intensity, the breather velocity generically locks at rational multiples of the
driving frequency. In most cases, the locking plateau coincides with the linear
stability domain of the resonant mobile breather and the desynchronization
occurs by regular appearance of type I intermittencies. However, some plateaux
also show chaotic mobile breathers with locked velocity in the locking region.
The addition of a small subharmonic driving tames the locked chaotic solution
and enhances the stability of resonant mobile breathers.


title:
The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on
  Billiards

abstract:
  In this work we address the question of proving the stability of elliptic
2-periodic orbits for strictly convex billiards. Eventhough it is part of a
widely accepted belief that ellipticity implies stability, classical theorems
show that the certainty of stability relies upon more fine conditions. We
present a review of the main results and general theorems and describe the
procedure to fullfill the supplementary conditions for strictly convex
billiards.


title: Testing for Chaos in Deterministic Systems with Noise

abstract:
  Recently, we introduced a new test for distinguishing regular from chaotic
dynamics in deterministic dynamical systems and argued that the test had
certain advantages over the traditional test for chaos using the maximal
Lyapunov exponent.
  In this paper, we investigate the capability of the test to cope with
moderate amounts of noisy data. Comparisons are made between an improved
version of our test and both the ``tangent space'' and ``direct method'' for
computing the maximal Lyapunov exponent. The evidence of numerical experiments,
ranging from the logistic map to an eight-dimensional Lorenz system of
differential equations (the Lorenz 96 system), suggests that our method is
superior to tangent space methods and that it compares very favourably with
direct methods.


title: Comment on "Soliton ratchets induced by excitation of internal modes"

abstract:
  Very recently Willis et al. [Phys. Rev. E {\bf 69}, 056612 (2004)] have used
a collective variable theory to explain the appearance of a nonzero energy
current in an ac driven, damped sine-Gordon equation. In this comment, we prove
rigorously that the time-averaged energy current in an ac driven nonlinear
Klein-Gordon system is strictly zero.


title: On $\tau$-function of conjugate nets

abstract:
  We study a potential introduced by Darboux to describe conjugate nets, which
within the modern theory of integrable systems can be interpreted as a
$\tau$-function. We investigate the potential using the non-local
$\bar\partial$ dressing method of Manakov and Zakharov, and we show that it can
be interpreted as the Fredholm determinant of an integral equation which
naturally appears within that approach. Finally, we give some arguments
extending that interpretation to multicomponent Kadomtsev-Petviashvili
hierarchy.


title:
Chaotic itinerancy and power-law residence time distribution in
  stochastic dynamical system

abstract:
  To study a chaotic itinerant motion among varieties of ordered states, we
propose a stochastic model based on the mechanism of chaotic itinerancy. The
model consists of a random walk on a half-line, and a Markov chain with a
transition probability matrix. To investigate the stability of attractor ruins
in the model, we analyze the residence time distribution of orbits at attractor
ruins. We show that the residence time distribution averaged by all attractor
ruins is given by the superposition of (truncated) power-law distributions, if
a basin of attraction for each attractor ruin has zero measure. To make sure of
this result, we carry out a computer simulation for models showing chaotic
itinerancy. We also discuss the fact that chaotic itinerancy does not occur in
coupled Milnor attractor systems if the transition probability among attractor
ruins can be represented as a Markov chain.


title: Scattering of solitons on resonance. Asymptotics and numeric simulations

abstract:
  We investigate a propagation of solitons for nonlinear Schr\"odinger equation
under small driving force. The driving force passes through the resonance. The
process of scattering on the resonance leads to changing of number of solitons.
After the resonance the number of solitons depends on the amplitude of the
driving force. The analytical results were obtained by WKB and matching method.
We bring two examples of numeric simulations for verifying obtained analytical
formulas.


title:
Experimental and theoretical study of the passively mode-locked
  Ytterbium-doped double-clad fiber laser

abstract:
  We consider an Yb-doped double-clad fiber laser in a unidirectional ring
cavity containing a polarizer placed between two half-wave plates. Depending on
the orientation of the phase plates, the laser operates in continuous,
Q-switch, mode-lock or unstable self-pulsing regime. An experimental study of
the stability of the mode locking regime is realized versus the orientation of
the half-wave plates. A model for the stability of self-mode-locking and cw
operation is developed starting from two coupled nonlinear Schrodinger
equations in a gain medium. The model is reduced to a master equation in which
the coefficients are explicitly dependent on the orientation angles of the
phase plates. Analytical solutions are given together with their stability
versus the angles.


title: Characteristic invariants and Darboux's method

abstract:
  We develop method that allows to derive reductions and solutions to
hyperbolic systems of partial differential equations. The method is based on
using functions that are constant in the direction of characteristics of the
system. These functions generalize well-known Riemann invariants. As
applications we consider the gas dynamics system and ideal magnetohydrodynamics
equations. In special cases we find solutions of these equations depending on
some arbitrary functions.


title:
Atom-Optics Billiards: Non-linear dynamics with cold atoms in optical
  traps

abstract:
  We present a new experimental system (the ``atom-optics billiard'') and
demonstrate chaotic and regular dynamics of cold, optically trapped atoms. We
show that the softness of the walls and additional optical potentials can be
used to manipulate the structure of phase space.


title: Phase-Space Structure for Narrow Planetary Rings

abstract:
  We address the occurrence of narrow planetary rings under the interaction
with shepherds. Our approach is based on a Hamiltonian framework of
non-interacting particles where open motion (escape) takes place, and includes
the quasi-periodic perturbations of the shepherd's Kepler motion with small and
zero eccentricity. We concentrate in the phase-space structure and establish
connections with properties like the eccentricity, sharp edges and narrowness
of the ring. Within our scattering approach, the organizing centers necessary
for the occurrence of the rings are stable periodic orbits, or more generally,
stable tori. In the case of eccentric motion of the shepherd, the rings are
narrower and display a gap which defines different components of the ring.


title:
On the classification of conditionally integrable evolution systems in
  (1+1) dimensions

abstract:
  We generalize earlier results of Fokas and Liu and find all locally analytic
(1+1)-dimensional evolution equations of order $n$ that admit an $N$-shock type
solution with $N\leq n+1$.
  To this end we develop a refinement of the technique from our earlier work
(A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we
completely characterized all (1+1)-dimensional evolution systems
$\bi{u}_t=\bi{F}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^n\bi{u}/\p x^n)$ that are
conditionally invariant under a given generalized (Lie--B\"acklund) vector
field $\bi{Q}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^k\bi{u}/\p x^k)\p/\p\bi{u}$ under
the assumption that the system of ODEs $\bi{Q}=0$ is totally nondegenerate.
Every such conditionally invariant evolution system admits a reduction to a
system of ODEs in $t$, thus being a nonlinear counterpart to quasi-exactly
solvable models in quantum mechanics.
  Keywords: Exact solutions, nonlinear evolution equations, conditional
integrability, generalized symmetries, reduction, generalized conditional
symmetries
  MSC 2000: 35A30, 35G25, 81U15, 35N10, 37K35, 58J70, 58J72, 34A34


title: Nonlinear photonic lattices in anisotropic nonlocal self-focusing media

abstract:
  We analyze theoretically and generate experimentally two-dimensional
nonlinear periodic lattices in a photorefractive medium. We demonstrate that
the light-induced periodically modulated nonlinear refractive index is highly
anisotropic and nonlocal, and it depends on the lattice orientation relative to
the crystal axis. We discuss stability of such induced photonic structures and
their guiding properties.


title: Random-phase spatial solitons in instantaneous nonlocal nonlinear media

abstract:
  We predict random-phase spatial solitons in instantaneous nonlocal nonlinear
media. The key mechanism responsible for self-trapping of such incoherent
wave-packets is played by the non-local (rather than the traditional
non-instantaneous) nature of the nonlinearity. This new kind of incoherent
solitons has profoundly different features than other incoherent solitons.


title:
Emergence of chaotic attractor and anti-synchronization for two coupled
  monostable neurons

abstract:
  The dynamics of two coupled piece-wise linear one-dimensional monostable maps
is investigated. The single map is associated with Poincare section of the
FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to
the appearance of chaotic attractor. The attractor exists in an invariant
region of phase space bounded by the manifolds of the saddle fixed point and
the saddle periodic point. The oscillations from the chaotic attractor have a
spike-burst shape with anti-phase synchronized spiking.


title: From ballistic to Brownian vortex motion in complex oscillatory media

abstract:
  We show that the breaking of the rotation symmetry of spiral waves in
two-dimensional complex (period-doubled or chaotic) oscillatory media by
synchronization defect lines (SDL) is accompanied by an intrinsic drift of the
pattern. Single vortex motion changes from ballistic flights at a well-defined
angle from the SDL to Brownian-like diffusion when the turbulent character of
the medium increases. It gives rise, in non-turbulent multi-spiral regimes, to
a novel ``vortex liquid''.


title: Size-Distribution Scaling in Clusters of Allelomimetic Agents

abstract:
  The allelomimesis clustering model is based on only two parameters: a local
parameter $\alpha$ that represents the probability of nearest-neighbor copying
and a global parameter $p$ that represents the fraction of unresponsive agents.
The model results into the formation of clusters of agents, the sizes of which
obey a distribution that is determined by the values of $\alpha$ and $p$.
Several experimental data are fitted by tuning the two parameters. In
particular, the significance of the value of $\alpha$ that corresponds to an
experimental data is discussed and is justified according to behavioral
context. Recommendations for possible extensions of the model are also
enumerated.


title: Polymer transport in random flow

abstract:
  The dynamics of polymers in a random smooth flow is investigated in the
framework of the Hookean dumbbell model. The analytical expression of the
time-dependent probability density function of polymer elongation is derived
explicitly for a Gaussian, rapidly changing flow. When polymers are in the
coiled state the pdf reaches a stationary state characterized by power-law
tails both for small and large arguments compared to the equilibrium length.
The characteristic relaxation time is computed as a function of the Weissenberg
number. In the stretched state the pdf is unstationary and exhibits
multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow
confirm the relevance of theoretical results obtained for the delta-correlated
model.


title: Numerical computation of travelling breathers in Klein-Gordon chains

abstract:
  We numerically study the existence of travelling breathers in Klein-Gordon
chains, which consist of one-dimensional networks of nonlinear oscillators in
an anharmonic on-site potential, linearly coupled to their nearest neighbors.
Travelling breathers are spatially localized solutions having the property of
being exactly translated by $p$ sites along the chain after a fixed propagation
time $T$ (these solutions generalize the concept of solitary waves for which
$p=1$). In the case of even on-site potentials, the existence of small
amplitude travelling breathers superposed on a small oscillatory tail has been
proved recently (G. James and Y. Sire, to appear in {\sl Comm. Math. Phys.},
2004), the tail being exponentially small with respect to the central
oscillation size. In this paper we compute these solutions numerically and
continue them into the large amplitude regime for different types of even
potentials. We find that Klein-Gordon chains can support highly localized
travelling breather solutions superposed on an oscillatory tail. We provide
examples where the tail can be made very small and is difficult to detect at
the scale of central oscillations. In addition we numerically observe the
existence of these solutions in the case of non even potentials.


title: $1/f^\alpha$ spectra in elementary cellular automata and fractal signals

abstract:
  We systematically compute the power spectra of the one-dimensional elementary
cellular automata introduced by Wolfram. On the one hand our analysis reveals
that one automaton displays $1/f$ spectra though considered as trivial, and on
the other hand that various automata classified as chaotic/complex display no
$1/f$ spectra. We model the results generalizing the recently investigated
Sierpinski signal to a class of fractal signals that are tailored to produce
$1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular
automata patterns in chemistry, physics and computer sciences, there are
various candidates to show spectra similar to our results.


title: Synchronization of fractional order chaotic systems

abstract:
  The chaotic dynamics of fractional order systems begin to attract much
attentions in recent years. In this brief report, we study the master-slave
synchronization of fractional order chaotic systems. It is shown that
fractional order chaotic systems can also be synchronized.


title:
Analytical calculation of slip flow in lattice Boltzmann models with
  kinetic boundary conditions

abstract:
  We present a mathematical formulation of kinetic boundary conditions for
Lattice Boltzmann schemes in terms of reflection, slip, and accommodation
coefficients. It is analytically and numerically shown that, in the presence of
a non-zero slip coefficient, the Lattice Boltzmann flow develops a physical
slip flow component at the wall. Moreover, it is shown that the slip
coefficient can be tuned in such a way to recover quantitative agreement with
analytical and experimental results up to second order in the Knudsen number.


title:
Tunneling of Bose-Einstein condensates and nonlinear models with
  separatrix crossings

abstract:
  This paper has been withdrawn by the author. Instead, more comprehensive and
accurate works are placed in: 1) cond-mat/0610767: Universality in nonadiabatic
behaviour of classical actions in nonlinear models with separatrix crossings,
to appear in Phys.Rev.E; and 2) nlin/0611007: Change in the adiabatic invariant
in a nonlinear two-mode model of Feshbach resonance passage, to appear in
Physica D


title: Fano resonance in quadratic waveguide arrays

abstract:
  We study resonant light scattering in arrays of channel optical waveguides
where tunable quadratic nonlinearity is introduced as nonlinear defects by
periodic poling of single (or several) waveguides in the array. We describe
novel features of wave scattering that can be observed in this structure and
show that it is a good candidate for the first observation of Fano resonance in
nonlinear optics.


title: Exact Solutions of Integrable 2D Contour Dynamics

abstract:
  A class of exact solutions of the dispersionless Toda hierarchy constrained
by a string equation is obtained. These solutions represent deformations of
analytic curves with a finite number of nonzero harmonic moments. The
corresponding tau-functions are determined and the emergence of cusps is
studied.


title:
Semiclassical orthogonal polynomials, matrix models and isomonodromic
  tau functions

abstract:
  The differential systems satisfied by orthogonal polynomials with arbitrary
semiclassical measures supported on contours in the complex plane are derived,
as well as the compatible systems of deformation equations obtained from
varying such measures. These are shown to preserve the generalized monodromy of
the associated rank-2 rational covariant derivative operators. The
corresponding matrix models, consisting of unitarily diagonalizable matrices
with spectra supported on these contours are analyzed, and it is shown that all
coefficients of the associated spectral curves are given by logarithmic
derivatives of the partition function or, more generally, the gap probablities.
The associated isomonodromic tau functions are shown to coincide, within an
explicitly computed factor, with these partition functions.


title:
Stabilization mechanism for two-dimensional solitons in nonlinear
  parametric resonance

abstract:
  We consider a simple model system supporting stable solitons in two
dimensions. The system is the parametrically driven damped nonlinear
Schr\"odinger equation, and the soliton stabilises for sufficiently strong
damping. The purpose of this note is to elucidate the stabilisation mechanism;
we do this by reducing the partial differential equation to a
finite-dimensional dynamical system. Our conclusion is that the negative
feedback loop occurs via the enslaving of the soliton's phase, locked to the
driver, to its amplitude and width.


title:
Solitary Wave Interactions In Dispersive Equations Using Manton's
  Approach

abstract:
  We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150},
397 (1979)] to compute solitary wave interactions in translationally invariant,
dispersive equations that support such localized solutions. The approach is
illustrated using as examples solitons in the Korteweg-de Vries equation,
standing waves in the nonlinear Schr{\"o}dinger equation and kinks as well as
breathers of the sine-Gordon equation.


title:
Integrable lattices and their sub-lattices: from the discrete Moutard
  (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

abstract:
  We introduce the sub-lattice approach, a procedure to generate, from a given
integrable lattice, a sub-lattice which inherits its integrability features. We
consider, as illustrative example of this approach, the discrete Moutard
4-point equation and its sub-lattice, the self-adjoint 5-point scheme on the
star of the square lattice, which are relevant in the theory of the integrable
Discrete Geometries and in the theory of discrete holomorphic and harmonic
functions (in this last context, the discrete Moutard equation is called
discrete Cauchy-Riemann equation). We use the sub-lattice point of view to
derive, from the Darboux transformations and superposition formulas of the
discrete Moutard equation, the Darboux transformations and superposition
formulas of the self-adjoint 5-point scheme. We also construct, from
algebro-geometric solutions of the discrete Moutard equation, algebro-geometric
solutions of the self-adjoint 5-point scheme. We finally use these solutions to
construct explicit examples of discrete holomorphic and harmonic functions, as
well as examples of quadrilateral surfaces in $\RR^3$.


title: On Some Classes of mKdV Periodic Solutions

abstract:
  We obtain exact periodic solutions of the positive and negative modified
Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these
solitary wave lattices through direct numerical simulations. While the positive
mKdV breather lattice solutions are found to be unstable, the two-soliton
lattice solution of the same equation is found to be stable. Similarly, a
negative mKdV lattice solution is found to be stable. We also touch upon the
implications of these results for the KdV equation.


title: Flow reversal in a simple dynamical model of turbulence

abstract:
  In this paper, we study a simple hydrodynamical model showing abrupt flow
reversals at random times. For a suitable range of parameters, we show that the
dynamics of flow reversal is accurately described by stochastic differential
equations, where the noise represents the effect of turbulence.


title:
Why nonlocal recursion operators produce local symmetries: new results
  and applications

abstract:
  It is well known that integrable hierarchies in (1+1) dimensions are local
while the recursion operators that generate them usually contain nonlocal
terms. We resolve this apparent discrepancy by providing simple and universal
sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions
to generate a hierarchy of local symmetries. These conditions are satisfied by
virtually all known today recursion operators and are much easier to verify
than those found in earlier work.
  We also give explicit formulas for the nonlocal parts of higher recursion
operators, Poisson and symplectic structures of integrable systems in (1+1)
dimensions.
  Using these two results we prove, under some natural assumptions, the
Maltsev--Novikov conjecture stating that higher Hamiltonian, symplectic and
recursion operators of integrable systems in (1+1) dimensions are weakly
nonlocal, i.e., the coefficients of these operators are local and these
operators contain at most one integration operator in each term.


title: Field theory of the inverse cascade in two-dimensional turbulence

abstract:
  A two-dimensional fluid, stirred at high wavenumbers and damped by both
viscosity and linear friction, is modeled by a statistical field theory. The
fluid's long-distance behavior is studied using renormalization-group (RG)
methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732
(1977)]. With friction, which dissipates energy at low wavenumbers, one expects
a stationary inverse energy cascade for strong enough stirring. While such
developed turbulence is beyond the quantitative reach of perturbation theory, a
combination of exact and perturbative results suggests a coherent picture of
the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is
derived from a generalized time-reversal symmetry and implies zero anomalous
dimension for the velocity even when friction is present. Thus the Kolmogorov
scaling of the inverse cascade cannot be explained by any RG fixed point. The
beta function for the dimensionless coupling ghat is computed through two
loops; the ghat^3 term is positive, as already known, but the ghat^5 term is
negative. An ideal cascade requires a linear beta function for large ghat,
consistent with a Pad\'e approximant to the Borel transform. The conjecture
that the Kolmogorov spectrum arises from an RG flow through large ghat is
compatible with other results, but the accurate k^{-5/3} scaling is not
explained and the Kolmogorov constant is not estimated. The lack of scale
invariance should produce intermittency in high-order structure functions, as
observed in some but not all numerical simulations of the inverse cascade. When
analogous RG methods are applied to the one-dimensional Burgers equation using
an FDT-preserving dimensional continuation, equipartition is obtained instead
of a cascade--in agreement with simulations.


title: Spatial coherence singularities and incoherent vortex solitons

abstract:
  We study spatially localized optical vortices created by self-trapping of
partially incoherent light with a phase dislocation in a biased photorefractive
crystal. In a contrast to the decay of coherent self-trapped vortex beams due
to the azimuthal instability, the incoherent vortices are stabilized when the
spatial incoherence of light exceeds a certain threshold. We analyze the
spatial coherence properties of the incoherent optical vortices and reveal the
existence of ring-like singularities in the spatial coherence function of a
vortex field that can characterize the stable propagation of vortices through
nonlinear media.


title: On Multiobjective Evolution Model

abstract:
  Self-Organized Criticality (SOC) phenomena could have a significant effect on
the dynamics of ecosystems. The Bak-Sneppen (BS) model is a simple and robust
model of biological evolution that exhibits punctuated equilibrium behavior.
Here we will introduce random version of BS model. Also we generalize the
single objective BS model to a multiobjective one.


title: Spatiotemporal discrete multicolor solitons

abstract:
  We have found various families of two-dimensional spatiotemporal solitons in
quadratically nonlinear waveguide arrays. The families of unstaggered odd, even
and twisted stationary solutions are thoroughly characterized and their
stability against perturbations is investigated. We show that the twisted and
even solutions display instability, while most of the odd solitons show
remarkable stability upon evolution.


title:
On Optimal Canonical Variables in the Theory of Ideal Fluid with Free
  Surface

abstract:
  Dynamics of ideal fluid with free surface can be effectively solved by
perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that
perturbation theory, which includes third and fourth order terms in the
Hamiltonian, results in the ill-posed equations because of short wavelength
instability. To fix that problem we introduce the canonical Hamiltonian
transform from original physical variables to new variables for which
instability is absent.

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


title: Coherence controlled soliton interactions

abstract:
  We demonstrate theoretically and subsequently observe in experiment a novel
type of soliton interaction when a pair of closely spaced spatial optical
solitons as a whole is made partially incoherent. We explain how the character
of the soliton interaction can be controlled by the total partial incoherence,
and show a possibility to change the soliton interaction from attractive to
repulsive, or vice versa, near a certain threshold in the coherence parameter.


title:
Diffusion of optical pulses in dispersion-shifted randomly birefringent
  optical fibers

abstract:
  An effect of polarization-mode dispersion, nonlinearity and random variation
of dispersion along an optical fiber on a pulse propagation in a randomly
birefringent dispersion-shifted optical fiber with zero average dispersion is
studied. An averaged pulse width is shown analytically to diffuse with
propagation distance for arbitrary strong pulse amplitude. It is found that
optical fiber nonlinearity can not change qualitatively a diffusion of pulse
width but can only modify a diffusion law which means that a root mean square
pulse width grows at least as a linear function of the propagation distance.


title: Presymplectic representation of bi-Hamiltonian chain

abstract:
  Liouville integrable systems, which have bi-Hamiltonian representation of the
Gel'fand-Zakharevich type, are considered. Bi-presymplectic representation of
one-Casimir bi-Hamiltonian chains and weakly bi-presymplectic representation of
multi-Casimir bi-Hamiltonian chains are constructed. The reduction procedure
for Poisson and presymplectic structures is presented.


title: Kraichnan model of passive scalar advection

abstract:
  A simple model of a passive scalar quantity advected by a Gaussian
non-solenoidal ("compressible") velocity field is considered. Large order
asymptotes of quantum-field expansions are investigated by instanton approach.
The existence of finite convergence radius of the series is proved, a position
and a type of the corresponding singularity of the series in the regularization
parameter are determined. Anomalous exponents of the main contributions to the
structural functions are resummed using new information about the series
convergence and two known orders of the expansion.


title: Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons

abstract:
  We consider effects of a periodic modulation of the nonlinearity coefficient
on fundamental and higher-order solitons in the one-dimensional NLS equation,
which is an issue of direct interest to Bose-Einstein condensates in the
context of the Feshbach-resonance control, and fiber-optic telecommunications
as concerns periodic compensation of the nonlinearity. We find from
simulations, and explain by means of a straightforward analysis, that the
response of a fundamental soliton to the weak perturbation is resonant, if the
modulation frequency $\omega $ is close to the intrinsic frequency of the
soliton. For higher-order $n$-solitons with $n=2$ and 3, the response to an
extremely weak perturbation is also resonant, if $\omega $ is close to the
corresponding intrinsic frequency. More importantly, a slightly stronger drive
splits the 2- or 3-soliton, respectively, into a set of two or three moving
fundamental solitons. The dependence of the threshold perturbation amplitude,
necessary for the splitting, on $\omega $ has a resonant character too.
Amplitudes and velocities of the emerging fundamental solitons are accurately
predicted, using exact and approximate conservation laws of the perturbed NLS
equation.


title:
Scattering of Solitons and Dark Solitons by Potential Walls in the
  Nonlinear Schroedinger Equation

abstract:
  Scattering of solitons and dark solitons by potential walls is studied in the
nonlinear Schroedinger equation under various conditions. We investigate the
conditions under which solitons are split into two solitons at the potential
wall. We find that a soliton can be trapped in an interspace between two
potential walls. A dark soliton can also be scattered at the potential wall.
Similarly to a bright soliton, a dark soliton can pass through more easily the
potential wall, as the width of the dark soliton is larger. A dark soliton can
run away spontaneously from an interspace between the two potential walls. We
also study the motion of a two-dimensional soliton in a two-dimensional quintic
nonlinear Schroedinger equation. We find the coherent tunneling through a
potential wall, and the refraction corresponding to Newton's refraction theory.