title: Integrable systems with quadratic nonlinearity in Fourier space

abstract:
  The Lax pair representation in Fourier space is used to obtain a list of
integrable scalar evolutionary equations with quadratic nonlinearity. The
famous systems of this type such as KdV, intermediate long-wave equation (ILW),
Camassa-Holm and A. Degasperis systems are represented in this list. Some new
systems are obtained as well. The generalizations on two-dimensional and
discrete systems are discussed.


title: Nonnormality and the localized control of extended systems

abstract:
  The idea of controlling the dynamics of spatially extended systems using a
small number of localized perturbations is very appealing - such a setup is
easy to implement in practice. However, when the distance between controllers
generating the perturbations becomes large, control fails due to increasing
sensitivity of the system to noise and nonlinearities. We show that this
failure is due to the fact that the evolution operator for the controlled
system becomes increasingly nonnormal as the distance between controllers
grows. This nonnormality is the result of control and can arise even for
systems whose evolution operator is normal in the absence of control.


title:
Contact Line Instability and Pattern Selection in Thermally Driven
  Liquid Films

abstract:
  Liquids spreading over a solid substrate under the action of various forces
are known to exhibit a long wavelength contact line instability. We use an
example of thermally driven spreading on a horizontal surface to study how the
stability of the flow can be altered, or patterns selected, using feedback
control. We show that thermal perturbations of certain spatial structure
imposed behind the contact line and proportional to the deviation of the
contact line from its mean position can completely suppress the instability.
Due to the presence of mean flow and a spatially nonuniform nature of spreading
liquid films the dynamics of disturbances is governed by a nonnormal evolution
operator, opening up a possibility of transient amplification and nonlinear
instabilities. We show that in the case of thermal driving the nonnormality can
be significant, especially for small wavenumber disturbances, and trace the
origin of transient amplification to a close alignment of a large group of
eigenfunctions of the evolution operator. However, for values of noise likely
to occur in experiments we find that the transient amplification is not
sufficiently strong to either change the predictions of the linear stability
analysis or invalidate the proposed control approach.

categories: nlin.PS math-ph math.MP math.OC physics.flu-dyn


title: Inverse problem for sl(2) lattices

abstract:
  We consider the inverse problem for periodic sl(2) lattices as a canonical
transformation from the separation to local variables. A new concept of a
factorized separation chain is introduced allowing to solve the inverse problem
explicitly. The method is applied to an arbitrary representation of the
corresponding Sklyanin algebra.


title:
Equilibrium and nonequilibrium solitons in a lossy split-step system
  with lumped amplification

abstract:
  We propose a more realistic version of the recently introduced split-step
model (SSM), which consists of periodically alternating dispersive and
nonlinear segments, by adding uniformly distributed loss and lumped gain to it.
In the case when the loss is exactly balanced by gain, a family of stable
equilibrium solitons (ESs) is found. Unless the system's period L is very
small, saturation is observed in the dependence of the amplitude of the
established ES vs. that of the initial pulse. Stable nonequilibrium solitons
(NESs) are found in the case when the gain slightly exceeds (by up to 3%) the
value necessary to balance the loss. The existence of NESs is possible as the
excessive energy pump is offset by permanent radiation loss, which is confirmed
by computation of the corresponding Poynting vector. Unlike ESs that form a
continuous family of solutions, NES is an isolated solution, which disappears
in the limit of small L, i.e., it cannot be found in the overpumped nonlinear
Schroedinger equation. Interactions between ESs turn out to be essentially the
same as in SSM without loss and gain, while interactions between NESs are
different: two NESs perturb each other by the radiation jets emanating from
them, even if they are separated by a large distance. Moving NESs survive
collisions, changing their velocities.


title: Solitons in a Three-Wave System with Intrinsic Linear Mixing and Walkoff

abstract:
  A modification of the usual Type-II second-harmonic-generation model is
proposed, which includes two additional features: linear conversion and walkoff
(group-velocity difference) between two components of the fundamental-frequency
(FF) wave. Physical interpretations of the model are possible in both temporal
and spatial domains. In the absence of the intrinsic walkoff, the linear mixing
makes real soliton solutions stable or unstable, depending on the relative sign
of the two FF components. Unstable solitons spontaneously re-arrange themselves
into stable ones. Fundamental solitons change their shape (in particular, they
develop chirp) but remain stable if the intrinsic walkoff is included. In
addition, quasi-stable double-humped solitary waves are found in the latter
case.


title: $A_{n-1}^{(1)}$ Reflection K-Matrices

abstract:
  We investigate the possible regular solutions of the boundary Yang-Baxter
equation for the vertex models associated with the $A_{n-1}^{(1)}$ affine Lie
algebra. We have classified them in two classes of solutions. The first class
consists of $n(n-1)/2$ K-matrix solutions with three free parameters. The
second class are solutions that depend on the parity of $n$. For $n$ odd there
exist $n$ reflection matrices with $2+[n/2]$ free parameters. It turns out that
for $n$ even there exist $n/2$ K-matrices with $2+n/2$ free parameters and
$n/2$ K-matrices with $1+n/2$ free parameters.


title:
Lagrangian Statistics and Temporal Intermittency in a Shell Model of
  Turbulence

abstract:
  We study the statistics of single particle Lagrangian velocity in a shell
model of turbulence. We show that the small scale velocity fluctuations are
intermittent, with scaling exponents connected to the Eulerian structure
function scaling exponents. The observed reduced scaling range is interpreted
as a manifestation of the intermediate dissipative range, as it disappears in a
Gaussian model of turbulence.


title: Matrix Integrals, Symmetric Functions theory and matrix integrals

abstract:
  We consider certain scalar product of symmetric functions which is
parameterized by a function $r$ and an integer $n$. One the one hand we have a
fermionic representation of this scalar product. On the other hand we get a
representation of this product with the help of multi-integrals. This gives
links between a theory of symmetric functions, soliton theory and models of
random matrices (such as a model of normal matrices).


title:
Dynamical effects induced by long range activation in a nonequilibrium
  reaction-diffusion system

abstract:
  We both show experimentally and numerically that the time scales separation
introduced by long range activation can induce oscillations and excitability in
nonequilibrium reaction-diffusion systems that would otherwise only exhibit
bistability. Namely, we show that the Chlorite-Tetrathionate reaction, where
autocatalytic species diffuses faster than the substrates, the spatial
bistability domain in the nonequilibrium phase diagram is extended with
oscillatory and excitability domains. A simple model and a more realistic model
qualitatively account for the observed behavior. The latter model provides
quantitative agreement with the experiments.


title: Modulo Three Problem With A Cellular Automaton Solution

abstract:
  An important global property of a bit string is the number of ones in it. It
has been found that the parity (odd or even) of this number can be found by a
sequence of deterministic, translational invariant cellular automata with
parallel update in succession for a total of O(N^2) time. In this paper, we
discover a way to check if this number is divisible by three using the same
kind of cellular automata in O(N^3) time. We also speculate that the method
described here could be generalized to check if it is divisible by four and
other positive integers.


title:
Discrete transformation for matrix 3-waves problem in three dimensional
  space

abstract:
  Discrete transformation for 3- waves problem is constructed in explicit form.
Generalization of this system on the matrix case in three dimensional space
together with corresponding discrete transformation is presented also.


title: Behaviour of boundary functions for quantum billiards

abstract:
  We study the behaviour of the normal derivative of eigenfunctions of the
Helmholtz equation inside billiards with Dirichlet boundary condition. These
boundary functions are of particular importance because they uniquely determine
the eigenfunctions inside the billiard and also other physical quantities of
interest. Therefore they form a reduced representation of the quantum system,
analogous to the Poincar\'e section of the classical system. For the normal
derivatives we introduce an equivalent to the standard Green function and
derive an integral equation on the boundary. Based on this integral equation we
compute the first two terms of the mean asymptotic behaviour of the boundary
functions for large energies. The first term is universal and independent of
the shape of the billiard. The second one is proportional to the curvature of
the boundary. The asymptotic behaviour is compared with numerical results for
the stadium billiard, different limacon billiards and the circle billiard, and
good agreement is found. Furthermore we derive an asymptotic completeness
relation for the boundary functions.


title:
On Equation for Initial Values in Theory of the Second Order Ordinary
  Differential Equations

abstract:
  We consider the properties of the second order nonlinear differential
equations b''= g(a,b,b') with the function g(a,b,b'=c) satisfying the following
nonlinear partial differential equation $$
  \frac{d^2 g_{cc}}{da^2}-g_{c}\frac{dg_{cc}}{da}-4\frac{dg_{bc}}{da}+ $$ $$
  +4g_{c}g_{bc}-3g_{b}g_{cc}+6g_{bb}=0, $$ where: $$
\frac{d}{da}=\frac{\partial}{\partial a}+c \frac{\partial}{\partial b}+ g
\frac{\partial}{\partial c}. $$
  Any equation b''=g(a,b,b') with this condition on function g(a,b,b') has the
General Integral F(a,b,x,y)=0 shared with General Integral of the second order
ODE's y''=f(x,y,y') with condition $\frac{\partial^4 f}{\partial y'^4}=0$ on
function f(x,y,y') or $$
y''+a_{1}(x,y)y'^3+3a_{2}(x,y)y'^2+3a_{3}(x,y)y'+a_{4}(x,y)=0 $$ with some
coefficients a_{i}(x,y).


title: The Riemann-Hilbert Problem for the Bi-Orthogonal Polynomials

abstract:
  For the bi-orthogonal polynomials with the third degree polynomial potential
functions, the 3 x 3 matrix Riemann-Hilbert problem is explicitly constructed.
The developed approach admits an extension to the bi-orthogonal polynomials
with arbitrary polynomial potentials.


title:
Riemann-Liouville integrals of fractional order and extended KP
  hierarchy

abstract:
  An attempt is given to formulate the extensions of the KP hierarchy by
introducing fractional order pseudo-differential operators. In the case of the
extension with the half-order pseudo-differential operators, a system analogous
to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the
supersymmetric extensions, no Grassmannian variable appears in the hierarchy
considered here. More general hierarchies constructed by the 1/N-th order
pseudo-differential operators, their integrability and the reduction procedure
are also investigated. In addition to finding out the new extensions of the KP
hierarchy, brief introduction to the Riemann-Liouville integral is provided to
yield a candidate for the fractional order pseudo-differential operators.


title:
Frequency Dependence of Quantum Localization in a Periodically Driven
  System

abstract:
  We study the quantum localization phenomena for a random matrix model
belonging to the Gaussian orthogonal ensemble (GOE). An oscillating external
field is applied on the system. After the transient time evolution, energy is
saturated to various values depending on the frequencies. We investigate the
frequency dependence of the saturated energy. This dependence cannot be
explained by a naive picture of successive independent Landau-Zener transitions
at avoided level crossing points. The effect of quantum interference is
essential. We define the number of Floquet states which have large overlap with
the initial state, and calculate its frequency dependence. The number of
Floquet states shows approximately linear dependence on the frequency, when the
frequency is small. Comparing the localization length in Floquet states and
that in energy states from the viewpoint of the Anderson localization, we
conclude that the Landau-Zener picture works for the local transition processes
between levels.


title: Fluctuations of wave functions about their classical average

abstract:
  Quantum-classical correspondence for the average shape of eigenfunctions and
the local spectral density of states are well-known facts. In this paper, the
fluctuations that quantum mechanical wave functions present around the
classical value are discussed. A simple random matrix model leads to a Gaussian
distribution of the amplitudes. We compare this prediction with numerical
calculations in chaotic models of coupled quartic oscillators. The expectation
is broadly confirmed, but deviations due to scars are observed.


title: Classical Mechanics of a Three Spin Cluster

abstract:
  A cluster of three spins coupled by single-axis anisotropic exchange exhibits
classical behaviors ranging from regular motion at low and high energies, to
chaotic motion at intermediate energies. A change of variable, taking advantage
of the conserved z-angular momentum, combined with a 3-d graphical presentation
(described in the Appendix), produce Poincare sections that manifest all
symmetries of the system and clearly illustrate the transition to chaos as
energy is increased.
  The three-spin system has four families of periodic orbits. Linearization
around stationary points predicts orbit periods in the low energy
(antiferromagnetic) and high energy (ferromagnetic) limits and also determines
the stability properties of certain orbits at a special intermediate energy.
The energy surface undergoes interesting changes of topology as energy is
varied. We describe the similiarities of our three spin system with the
Anisotropic Kepler Problem and the Henon-Heiles Hamiltonian. An appendix
discusses numerical integration techniques for spin systems.


title:
On the Nonlocal Equations and Nonlocal Charges Associated with the Harry
  Dym Hierarchy

abstract:
  A large class of nonlocal equations and nonlocal charges for the Harry Dym
hierarchy is exhibited. They are obtained from nonlocal Casimirs associated
with its bi-Hamiltonian structure. The Lax representation for some of these
equations is also given.


title: Dispersionless Limit of Integrable Models

abstract:
  Nonlinear dispersionless equations arise as the dispersionless limit of well
know integrable hierarchies of equations or by construction, such as the system
of hydrodynamic type. Some of these equations are integrable in the Hamiltonian
sense and appear in the study of topological minimal models. In the first part
of the review we will give a brief introduction to integrable models, mainly
its Lax representation. Then, we will introduce the dispersionless limit and
show some of our results concerning the two-component hyperbolic system of
equations such as the polytropic gas and Born-Infeld equations.


title:
Analytical perturbative approach to periodic orbits in the homogeneous
  quartic oscillator potential

abstract:
  We present an analytical calculation of periodic orbits in the homogeneous
quartic oscillator potential. Exploiting the properties of the periodic
Lam{\'e} functions that describe the orbits bifurcated from the fundamental
linear orbit in the vicinity of the bifurcation points, we use perturbation
theory to obtain their evolution away from the bifurcation points. As an
application, we derive an analytical semiclassical trace formula for the
density of states in the separable case, using a uniform approximation for the
pitchfork bifurcations occurring there, which allows for full semiclassical
quantization. For the non-integrable situations, we show that the uniform
contribution of the bifurcating period-one orbits to the coarse-grained density
of states competes with that of the shortest isolated orbits, but decreases
with increasing chaoticity parameter $\alpha$.


title:
Localized Waves without the Existence of Extended Waves: Oscillatory
  Convection of Binary Mixtures with Strong Soret Effect

abstract:
  Spatially confined solutions of traveling convection rolls are determined
numerically for binary mixtures like ethanol-water. The appropriate field
equations are solved in a vertical crossection of the rolls perpendicular to
their axes subject to realistic horizontal boundary conditions. The localized
convective states are stably and robustly sustained by strongly nonlinear
mixing and complex flow-induced concentration redistribution. We elucidate how
this enables their existence for strongly negative separation ratios at small
subcritical heating rates below the saddle-node of extended traveling
convection rolls where the quiescent fluid is strongly stable.


title: Energy Spectrum of Quasi-Geostrophic Turbulence

abstract:
  We consider the energy spectrum of a quasi-geostrophic model of forced,
rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2}
valid for wave numbers that are smaller than a wave number associated to the
forcing injection scale. This upper bound separates this spectrum from the
Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a
two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical
support for the k^{-2} spectrum observed in recent experiments.


title:
Deformation of surfaces, integrable systems and Self-Dual Yang-Mills
  equation

abstract:
  We conjecture that many (maybe all) integrable equations and spin systems in
2+1 dimensions can be obtained from the (2+1)-dimensional
Gauss-Mainardi-Codazzi and Gauss-Weingarten equations, respectively. We also
show that the (2+1)-dimensional Gauss-Mainardi-Codazzi equation which describes
the deformation (motion) of surfaces is the exact reduction of the
Yang-Mills-Higgs-Bogomolny and Self-Dual Yang-Mills equations. On the basis of
this observation, we suggest that the (2+1)-dimensional Gauss-Mainardi-Codazzi
equation is a candidate to be integrable and the associated linear problem (Lax
representation) with the spectral parameter is presented.


title:
A class of cellular automata equivalent to deterministic particle
  systems

abstract:
  We demonstrate that a local mapping f in a space of bisequences over {0,1}
which conserves the number of nonzero sites can be viewed as a deterministic
particle system evolving according to a local mapping in a space of increasing
bisequences over Z. We present an algorithm for determination of the local
mapping in the space of particle coordinates corresponding to the local mapping
f.


title: Individual-based lattice model for spatial spread of epidemics

abstract:
  We present a lattice gas cellular automaton (LGCA) to study spatial and
temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type.
The automaton is fully discrete, i.e. space, time and number of individuals are
discrete variables. The automaton can be applied to study spread of epidemics
in both human and animal populations. We investigate effects of spatial
inhomogeneities in initial distribution of infected and vaccinated populations
on the dynamics of epidemic of SIR type. We discuss vaccination strategies
which differ only in spatial distribution of vaccinated individuals. Also, we
derive an approximate, mean-field type description of the automaton, and
discuss differences between the mean-field dynamics and the results of LGCA
simulation.


title: Quantum Graphs: A simple model for Chaotic Scattering

abstract:
  We connect quantum graphs with infinite leads, and turn them to scattering
systems. We show that they display all the features which characterize quantum
scattering systems with an underlying classical chaotic dynamics: typical
poles, delay time and conductance distributions, Ericson fluctuations, and when
considered statistically, the ensemble of scattering matrices reproduce quite
well the predictions of appropriately defined Random Matrix ensembles. The
underlying classical dynamics can be defined, and it provides important
parameters which are needed for the quantum theory. In particular, we derive
exact expressions for the scattering matrix, and an exact trace formula for the
density of resonances, in terms of classical orbits, analogous to the
semiclassical theory of chaotic scattering. We use this in order to investigate
the origin of the connection between Random Matrix Theory and the underlying
classical chaotic dynamics. Being an exact theory, and due to its relative
simplicity, it offers new insights into this problem which is at the fore-front
of the research in chaotic scattering and related fields.


title: Landau damping of partially incoherent Langmuir waves

abstract:
  It is shown that partial incoherence, in the form of stochastic phase noise,
of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type
damping. Starting from the Zakharov equations, which describe the nonlinear
interaction between Langmuir and ion-acoustic waves, a kinetic equation is
derived for the plasmons by introducing the Wigner-Moyal transform of the
complex Langmuir wave field. This equation is then used to analyze the
stability properties of small perturbations on a stationary solution consisting
of a constant amplitude wave with stochastic phase noise. The concomitant
dispersion relation exhibits the phenomenon of Landau-like damping. However,
this damping differs from the classical Landau damping in which a Langmuir
wave, interacting with the plasma electrons, loses energy. In the present
process, the damping is non-dissipative and is caused by the resonant
interaction between an instantaneously-produced disturbance, due to the
parametric interactions, and a partially incoherent Langmuir wave, which can be
considered as a quasi-particle composed of an ensemble of partially incoherent
plasmons.


title:
Random Matrices close to Hermitian or unitary: overview of methods and
  results

abstract:
  The paper discusses progress in understanding statistical properties of
complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and
non-Hermitian random matrices. Ensembles of this type emerge in various
physical contexts, most importantly in random matrix description of quantum
chaotic scattering as well as in the context of QCD-inspired random matrix
models.


title:
Envelope solitons induced by high-order effects of light-plasma
  interaction

abstract:
  The nonlinear coupling between the light beams and non-resonant ion density
perturbations in a plasma is considered, taking into account the relativistic
particle mass increase and the light beam ponderomotive force. A pair of
equations comprising a nonlinear Schrodinger equation for the light beams and a
driven (by the light beam pressure) ion-acoustic wave response is derived. It
is shown that the stationary solutions of the nonlinear equations can be
represented in the form of a bright and dark/gray soliton for one-dimensional
problem. We have also present a numerical analysis which shows that our bright
soliton solutions are stable exclusively for the values of the parameters
compatible with of our theory.


title: Scale by scale budget and similarity laws for shear turbulence

abstract:
  Turbulent shear flows, such as those occurring in the wall region of
turbulent boundary layers, manifest a substantial increase of intermittency
with respect to isotropic conditions. This suggests a close link between
anisotropy and intermittency. However, a rigorous statistical description of
anisotropic flows is, in most cases, hampered by the inhomogeneity of the
field. This difficulty is absent for the homogeneous shear flow. For this flow
the scale by scale budget is discussed here by using the appropriate form of
the Karman-Howarth equation, to determine the range of scales where the shear
is dominant. The issuing generalization of the four-fifths law is then used as
the guideline to extend to shear dominated flows the Kolmogorov-Obhukhov theory
of intermittency. The procedure leads naturally to the formulation of
generalized structure functions and the description of intermittency thus
obtained reduces to the K62 theory for vanishing shear. Also here the
intermittency corrections to the scaling exponents are carried by the moments
of the coarse grained energy dissipation field. Numerical experiments give
indications that the dissipation field is statistically unaffected by the
shear, thereby supporting the conjecture that the intermittency corrections are
universal. This observation together with the present reformulation of the
theory gives reason for the increased intermittency observed in the classical
longitudinal velocity increments.


title:
Envelope Solitons of Nonlinear Schrodinger Equation with an Anti-cubic
  Nonlinearity

abstract:
  On the basis of a recently-proposed method to find solitary solutions of
generalized nonlinear Schrodinger equations [1]-[3], the existence of an
envelope solitonlike solutions of a nonlinear Schrodinger equation containing
an anti-cubic nonlinearity (|Psi|^{-4} Psi) plus a "regular" nonlinear part is
investigated. In particular, in case the regular nonlinear part consists of a
sum of a cubic and a quintic nonlinearities (i.e. q_1 |Psi|^2 Psi + q_2 |Psi|^4
Psi), an upper-shifted bright envelope solitonlike solution is explicitly
found.


title: Adaptive learning and coloniality in birds

abstract:
  We introduce here three complementary models to analyze the role of predation
pressure in avian coloniality. Different explanations have been proposed for
the existence of colonial breeding behavior in birds, but field studies offer
no conclusive results. We first propose a learning model in which the decision
of birds are taken according to the collective performance. The properties of
the system are then studied according to a model in which birds choose
according to their individual experience, and the agreement of the introduction
of spatial structure with field data are then shown.


title:
Induced defect nucleation and side-band instabilities in hexagons with
  rotation and mean flow

abstract:
  The combined effect of mean flow and rotation on hexagonal patterns is
investigated using Ginzburg-Landau equations that include nonlinear gradient
terms as well as the nonlocal coupling provided by the mean flow. Long-wave and
short-wave side-band instabilities are determined. Due to the nonlinear
gradient terms and enhanced by the mean flow, the penta-hepta defects can
become unstable to the induced nucleation of dislocations in the defect-free
amplitude, which can lead to the proliferation of penta-hepta defects and
persistent spatio-temporal chaos. For individual penta-hepta defects the
nonlinear gradient terms enhance climbing or gliding motion, depending on
whether they break the chiral symmetry or not.

categories: nlin.CD cond-mat.soft nlin.PS physics.flu-dyn


title: Tomography of Solitons

abstract:
  We develope the tomographic representation ofwavefunctions which are
solutions of the generalizednonlinear Schrodinger equation (NLSE) and show
itsconnection with the Weyl--Wigner map.In particular, this theory is applied
tothe envelope solitons, where tomograms for envelopebright solitons of a wide
family of modified NLSE arepresented and numerically evalueted.


title: Soluble models of turbulent advection

abstract: Introductory lectures on the Kraichnan model of passive advection


title: Parallelization of Cellular Automata for Surface Reactions

abstract:
  We present a parallel implementation of cellular automata to simulate
chemical reactions on surfaces. The scaling of the computer time with the
number of processors for this parallel implementation is quite close to the
ideal T/P, where T is the computer time used for one single processor and P the
number of processors. Two examples are presented to test the algorithm, the
simple A+B->0 model and a realistic model for CO oxidation on Pt(110). By using
large parallel simulations, it is possible to derive scaling laws which allow
us to extrapolate to even larger system sizes and faster diffusion coefficients
allowing us to make direct comparisons with experiments.

categories: nlin.CG cond-mat.mtrl-sci nlin.PS physics.comp-ph


title: Scarred eigenstates for quantum cat maps of minimal periods

abstract:
  In this paper we construct a sequence of eigenfunctions of the ``quantum
Arnold's cat map'' that, in the semiclassical limit, show a strong scarring
phenomenon on the periodic orbits of the dynamics. More precisely, those states
have a semiclassical limit measure that is the sum of 1/2 the normalized
Lebesgue measure on the torus plus 1/2 the normalized Dirac measure
concentrated on any a priori given periodic orbit of the dynamics. It is known
(the Schnirelman theorem) that ``most'' sequences of eigenfunctions
equidistribute on the torus. The sequences we construct therefore provide an
example of an exception to this general rule. Our method of construction and
proof exploits the existence of special values of Planck's constant for which
the quantum period of the map is relatively ``short'', and a sharp control on
the evolution of coherent states up to this time scale. We also provide a
pointwise description of these states in phase space, which uncovers their
``hyperbolic'' structure in the vicinity of the fixed points and yields more
precise localization estimates.


title: Termination of Reentry in an Inhomogeneous Ring of Model Cardiac Cells

abstract:
  Reentrant waves propagating in a ring or annulus of excitable media model is
the basic mechanism underlying a major class of irregular cardiac rhythms known
as anatomical reentry. Such reentrant waves are terminated by rapid electrical
stimulation (pacing) from an implantable device. Because the mechanisms of such
termination are poorly understood, we study pacing of anatomical reentry in a
one-dimensional ring of model cardiac cells. For realistic off-circuit pacing,
our model-independent results suggest that circuit inhomogeneities, and the
electrophysiological dynamical changes they introduce, may be essential for
terminating reentry in some cases.


title:
Stationary modulated-amplitude waves in the 1-D complex Ginzburg-Landau
  equation

abstract:
  We reformulate the one-dimensional complex Ginzburg-Landau equation as a
fourth order ordinary differential equation in order to find stationary
spatially-periodic solutions. Using this formalism, we prove the existence and
stability of stationary modulated-amplitude wave solutions. Approximate
analytic expressions and a comparison with numerics are given.


title:
Differential systems for biorthogonal polynomials appearing in 2-matrix
  models and the associated Riemann-Hilbert problem

abstract:
  We consider biorthogonal polynomials that arise in the study of a
generalization of two--matrix Hermitian models with two polynomial potentials
V_1(x), V_2(y) of any degree, with arbitrary complex coefficients. Finite
consecutive subsequences of biorthogonal polynomials (`windows'), of lengths
equal to the degrees of the potentials, satisfy systems of ODE's with
polynomial coefficients as well as PDE's (deformation equations) with respect
to the coefficients of the potentials and recursion relations connecting
consecutive windows. A compatible sequence of fundamental systems of solutions
is constructed for these equations. The (Stokes) sectorial asymptotics of these
fundamental systems are derived through saddle-point integration and the
Riemann-Hilbert problem characterizing the differential equations is deduced.


title:
On the stability of classical chaotic motion under system's
  perturbations

abstract:
  We study in detail the time behavior of classical fidelity for chaotic
systems. We show in particular that the asymptotic decay, depending on system
dynamical properties, can be either exponential, with a rate determined by the
gap in the discretized Perron-Frobenius operator, or algebraic, with the same
power as for correlation functions decay. Therefore the decay of fidelity is
strictly connected to correlations decay.


title: Local 4/5-Law and Energy Dissipation Anomaly in Turbulence

abstract:
  A strong local form of the ``4/3-law'' in turbulent flow has been proved
recently by Duchon and Robert for a triple moment of velocity increments
averaged over both a bounded spacetime region and separation vector directions,
and for energy dissipation averaged over the same spacetime region. Under
precisely stated hypotheses, the two are proved to be proportional, by a
constant 4/3, and to appear as a nonnegative defect measure in the local energy
balance of singular (distributional) solutions of the incompressible Euler
equations. Here we prove that the energy defect measure can be represented also
by a triple moment of purely longitudinal velocity increments and by a mixed
moment with one longitudinal and two tranverse velocity increments. Thus, we
prove that the traditional 4/5- and 4/15-laws of Kolmogorov hold in the same
local sense as demonstrated for the 4/3-law by Duchon-Robert.


title:
Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II --
  Spheroidal Cavity --

abstract:
  We derive a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences and
discontinuities occurring at bifurcation points and in the spherical limit, the
trace integrals over the action-angle variables are performed using an improved
stationary phase method. The resulting semiclassical level density oscillations
and shell energies are in good agreement with quantum-mechanical results. We
find that the births of three-dimensional orbits through the bifurcations of
planar orbits in the equatorial plane lead to considerable enhancement of shell
effect for superdeformed shapes.


title: Prolongation structure of the Krichever-Novikov equation

abstract:
  We completely describe Wahlquist-Estabrook prolongation structures
(coverings) dependent on u, u_x, u_{xx}, u_{xxx} for the Krichever-Novikov
equation u_t=u_{xxx}-3u_{xx}^2/(2u_x)+p(u)/u_x+au_x in the case when the
polynomial p(u)=4u^3-g_2u-g_3 has distinct roots. We prove that there is a
universal prolongation algebra isomorphic to the direct sum of a commutative
2-dimensional algebra and a certain subalgebra of the tensor product of sl_2(C)
with the algebra of regular functions on an affine elliptic curve. This is
achieved by identifying this prolongation algebra with the one for the
anisotropic Landau-Lifshitz equation. Using these results, we find for the
Krichever-Novikov equation a new zero-curvature representation, which is
polynomial in the spectral parameter in contrast to the known elliptic ones.


title:
Proof of the generalized Lieb-Wehrl conjecture for integer indices
  larger than one

abstract:
  Gnutzmann and Zyczkowski have proposed the Renyi-Wehrl entropy as a
generalization of the Wehrl entropy, and conjectured that its minimum is
obtained for coherent states. We prove this conjecture for the Renyi index
q=2,3,... in the cases of compact semisimple Lie groups. A general formula for
the minimum value is given.


title: Rayleigh-Benard Convection with a Radial Ramp in Plate Separation

abstract:
  Pattern formation in Rayleigh-Benard convection in a large-aspect-ratio
cylinder with a radial ramp in the plate separation is studied analytically and
numerically by performing numerical simulations of the Boussinesq equations. A
horizontal mean flow and a vertical large scale counterflow are quantified and
used to understand the pattern wavenumber. Our results suggest that the mean
flow, generated by amplitude gradients, plays an important role in the roll
compression observed as the control parameter is increased. Near threshold the
mean flow has a quadrupole dependence with a single vortex in each quadrant
while away from threshold the mean flow exhibits an octupole dependence with a
counter-rotating pair of vortices in each quadrant. This is confirmed
analytically using the amplitude equation and Cross-Newell mean flow equation.
By performing numerical experiments the large scale counterflow is also found
to aid in the roll compression away from threshold but to a much lesser degree.
Our results yield an understanding of the pattern wavenumbers observed in
experiment away from threshold and suggest that near threshold the mean flow
and large scale counterflow are not responsible for the observed shift to
smaller than critical wavenumbers.


title: Localized transverse bursts in inclined layer convection

abstract:
  We investigate a novel bursting state in inclined layer thermal convection in
which convection rolls exhibit intermittent, localized, transverse bursts. With
increasing temperature difference, the bursts increase in duration and number
while exhibiting a characteristic wavenumber, magnitude, and size. We propose a
mechanism which describes the duration of the observed bursting intervals and
compare our results to bursting processes in other systems.


title:
Dynamo effect beyond the kinematic approximation: suppression of linear
  instabilities by non-linear feedback

abstract:
  The turbulent dynamo effect, which describes the generation of magnetic
fields in astrophysical objects, is described by the dynamo equation. This, in
the kinematic (linear) approximation gives an unbounded exponential growth of
the long wavelength part of the magnetic fields. Here we, in a systematic
diagrammatic, perturbation theory, show how non-linear effects suppress the
linear instability and bring down the growth rate to zero in the large time
limit. We work with diffferent background velicity spectrum and initial
magnetic field correlations. Our results indicate the robustness and very
general nature of dynamo growth: It is qualitatively independent of the
background velicty and intial magnetic field spectra. We also argue that our
results can be justified within the framework of the first order smoothing
approximation, as applicable for the full non-linear problem. We discuss our
results from the view points of renormalisation group analysis.


title: Hierarchy of Chaotic maps with an invariant measure and their coupling

abstract:
  Hierarchy of one-parameter families of chaotic maps with an invariant measure
have been introduced, where their appropriate coupling has lead to the
generation of some coupled chaotic maps with an invariant measure. It is shown
that these chaotic maps (also the coupled maps) do not undergo any period
doubling or period-n-tupling cascade bifurcation to chaos, but they have either
single fixed point attractor at certain values of the parameters or they are
ergodic in the complementary region. Using the invariant measure or
Sinai-Rulle-Bowen measure the Kolmogrov-Sinai entropy of the chaotic maps
(coupled maps) have been calculated analytically, where the numerical
simulations support the results


title: On the Global Dynamics of the Anisotropic Manev Problem

abstract:
  We study the global flow of the anisotropic Manev problem, which describes
the planar motion of two bodies under the influence of an anisotropic Newtonian
potential with a relativistic correction term. We first find all the
heteroclinic orbits between equilibrium solutions. Then we generalize the
Poincare'-Melnikov method and use it to prove the existence of infinitely many
transversal homoclinic orbits. Invoking a variational principle and the
symmetries of the system, we finally detect infinitely many classes of periodic
orbits.


title:
Crossover of quantum Loschmidt echo from golden rule decay to
  perturbation-independent decay

abstract:
  We study the crossover of the quantum Loschmidt echo (or fidelity) from the
golden rule regime to the perturbation-independent exponential decay regime by
using the kicked top model. It is shown that the deviation of the
perturbation-independent decay of the averaged fidelity from the Lyapunov decay
results from quantum fluctuations in individual fidelity, which are caused by
the coherence in the initial coherent states.
  With an averaging procedure suppressing the quantum fluctuations effectively,
the perturbation-independent decay is found to be close to the Lyapunov decay.
  We also show that the Fourier transform of the fidelity is determined
directly by the initial state and the eigenstates of the Floquet operators of
the two classically chaotic systems concerned.
  The absolute value part and the phase part of the Fourier transform of the
fidelity are found to be divided into several correlated parts, which is a
manifestation of the coherence of the initial coherent state.
  In the whole crossover region, some important properties of the fidelity,
such as the exponent of its exponential decay and the short initial time within
which the fidelity almost does not change, are found to be closely related to
properties of the central part of its Fourier transform.


title:
Demonstration of the stability or instability of multibreathers at low
  coupling

abstract:
  Whereas there exists a mathematical proof for one--site breathers stability,
and an unpublished one for two--sites breathers, the methods for determining
the stability properties of multibreathers rely in numerical computation of the
Floquet multipliers or in the weak nonlinearity approximation leading to
discrete non--linear Schr\"odinger equations. Here we present a set of
multibreather stability theorems (MST) that provides with a simple method to
determine multibreathers stability in Klein--Gordon systems. These theorems are
based in the application of degenerate perturbation theory to Aubry's band
theory. We illustrate them with several examples.


title:
Convective and absolute Eckhaus instability leading to modulated waves
  in a finite box

abstract:
  We report experimental study of the secondary modulational instability of a
one-dimensional non-linear traveling wave in a long bounded channel. Two
qualitatively different instability regimes involving fronts of spatio-temporal
defects are linked to the convective and absolute nature of the instability.
Both transitions appear to be subcritical. The spatio-temporal defects control
the global mode structure.


title:
Homogeneous isotropic turbulence in dilute polymers: scale by scale
  budget

abstract:
  The turbulent energy cascade in dilute polymers solution is addressed here by
considering a direct numerical simulation of homogeneous isotropic turbulence
of a FENE-P fluid in a triply periodic box. On the basis of the DNS data, a
scale by scale analysis is provided by using the proper extension to
visco-elastic fluids of the Karman-Howarth equation for the velocity. For the
microstructure, an equation, analogous to the Yaglom equation for scalars, is
proposed for the free-energy density associated to the elastic behavior of the
material. Two mechanisms of energy removal from the scale of the forcing are
identified, namely the classical non-linear transfer term of the standard
Navier-Stokes equations and the coupling between macroscopic velocity and
microstructure. The latter, on average, drains kinetic energy to feed the
dynamics of the microstructure. The cross-over scale between the two
corresponding energy fluxes is identified, with the flux associated with the
microstructure dominating at small separations to become sub-leading above the
cross-over scale, which is the equivalent of the elastic limit scale defined by
De Gennes-Tabor on the basis of phenomenological assumptions.


title: A New Paradigm in Chaotic Ray Scattering

abstract:
  We introduce a new paradigm of 2D (electromagnetic) ray-chaos, featuring both
guided and scattered rays in a dielectric layer with exponentially tapered
refraction index backed by an undulated conductive surface, and illustrate its
relevant features. Numerical simulations of the corresponding full-wave
solution indicate that the system complies with Berry's conjecture in the
asymptotic short wavelength limit.


title:
3D BEC Bright Solitons under Transverse Confinement: Analytical Results
  with the Nonpolynomial Schrodinger Equation

abstract:
  The Bose-Einstein condensate (BEC) of a dilute gas of bosons is well
described by the three-dimensional Gross-Pitaevskii equation (3D GPE), that is
a nonlinear Schrodinger equation. By imposing a transverse confinement the BEC
can travel only in the cylindrical axial direction. We show that in this case
the BEC with attractive interaction admits a 3D bright soliton solution which
generalizes the text-book one, that is valid in the one-dimensional limit (1D
GPE). Contrary to the 1D case, the 3D bright soliton exists only below a
critical number of Bosons that depends on the extent of confinement. Finally,
we find that the 3D bright soliton collapses if its density excedes a critical
value. Our results are obtained by using a nonpolynomial Schrodinger equation
(NPSE), an effective one-dimensional equation derived from the 3D GPE.


title: Fractal Weyl laws for chaotic open systems

abstract:
  We present a result relating the density of quantum resonances for an open
chaotic system to the fractal dimension of the associated classical repeller.
The result is supported by numerical computation of the resonances of the
system of n disks on a plane. The result generalizes the Weyl law for the
density of states of a closed system to chaotic open systems.


title:
The Lattice Equations of the Toda Type with an Interaction between a Few
  Neighborhoods

abstract:
  The sets of the integrable lattice equations, which generalize the Toda
lattice, are considered. The hierarchies of the first integrals and
infinitesimal symmetries are found. The properties of the multi-soliton
solutions are discussed.


title: Real-Valued Algebro-Geometric Solutions of the Camassa--Holm hierarchy

abstract:
  We provide a treatment of real-valued, smooth, and bounded algebro-geometric
solutions of the Camassa--Holm (CH) hierarchy and describe the associated
isospectral torus. We also discuss real-valued algebro-geometric solutions with
a cusp behavior.


title:
Using of Phenomenological Piecewise Continuous Map for Modeling of
  Neurons Behaviour

abstract:
  A piecewise continuous map for modeling bursting and spiking behaviour of
isolated neuron is proposed. The map was created from phenomenological
viewpoint. The map demonstrates oscillations, which are qualitatively similar
to oscillations generating by Rose-Hindmarsh model. The synchronization in
small ensembles of the maps is investigated. It is considered the different
number of elements in the ensemble and different connectivity topologies.


title: Survival and Extinction in Cyclic and Neutral Three--Species Systems

abstract:
  We study the ABC model (A + B --> 2B, B + C --> 2C, C + A --> 2A), and its
counterpart: the three--component neutral drift model (A + B --> 2A or 2B, B +
C --> 2B or 2C, C + A --> 2C or 2A.) In the former case, the mean field
approximation exhibits cyclic behaviour with an amplitude determined by the
initial condition. When stochastic phenomena are taken into account the
amplitude of oscillations will drift and eventually one and then two of the
three species will become extinct. The second model remains stationary for all
initial conditions in the mean field approximation, and drifts when stochastic
phenomena are considered. We analyzed the distribution of first extinction
times of both models by simulations and from the point of view of the
Fokker-Planck equation. Survival probability vs. time plots suggest an
exponential decay. For the neutral model the extinction rate is inversely
proportional to the system size, while the cyclic model exhibits anomalous
behaviour for small system sizes. In the large system size limit the extinction
times for both models will be the same. This result is compatible with the
smallest eigenvalue obtained from the numerical solution of the Fokker-Planck
equation. We also studied the long--time behaviour of the probability
distribution. The exponential decay is found to be robust against certain
changes, such as the three reactions having different rates.


title:
Hierarchy of one and many-parameter families of elliptic chaotic maps of
  cn and sn types

abstract:
  We present hierarchy of one and many-parameter families of elliptic chaotic
maps of cn and sn types at the interval [0,1]. It is proved that for small
values of k the parameter of the elliptic function, these maps are
topologically conjugate to the maps of references [1,2], where using this we
have been able to obtain the invariant measure of these maps for small k and
thereof it is shown that these maps have the same Kolmogorov-Sinai entropy or
equivalently Lyapunov characteristic exponent of the maps of references [1,2]}.
As this parameter vanishes, the maps are reduced to the maps presented in
above-mentioned reference. Also in contrary to the usual family of
one-parameter maps, such as the logistic and tent maps, these maps do not
display period doubling or period-n-tupling cascade transition to chaos, but
they have single fixed point attractor at certain parameter values where they
bifurcate directly to chaos without having period-n-tupling scenario exactly at
these values of parameters whose Lyapunov characteristic exponent begin to be
positive.


title: On generating functions in the AKNS hierarchy

abstract:
  It is shown that the self-induced transparency equations can be interpreted
as a generating function for as positive so negative flows in the AKNS
hierarchy. Mutual commutativity of these flows leads to other hierarchies of
integrable equations. In particular, it is shown that stimulated Raman
scattering equations generate the hierarchy of flows which include the
Heisenberg model equations. This observation reveals some new relationships
between known integrable equations and permits one to construct their new
physically important combinations. Reductions of the AKNS hierarchy to ones
with complex conjugate and real dependent variables are also discussed and the
corresponding generating functions of positive and negative flows are found.
Generating function of Whitham modulation equations in the AKNS hierarchy is
obtained.


title:
Scaling at the onset of chaos in a network of logistic maps with two
  types of global coupling

abstract:
  We study a network of logistic maps with two types of global coupling,
inertial and dissipative. Features of the clusterization process are revealed
and compared, which are associated with presence of each type of couplings. For
the parameter region near the onset of chaos we outline scaling properties in
dynamical behavior of the network and illustrate them on the Kaneko phase
diagrams.


title: Mean effects of turbulence on elliptic instability in fluids

abstract:
  Elliptic instability in fluids is discussed in the context of the
Lagrangian-averaged Navier-Stokes-alpha (LANS$-\alpha$) turbulence model. This
model preserves the Craik-Criminale (CC) family of solutions consisting of a
columnar eddy and a Kelvin wave. The LANS$-\alpha$ model is shown to preserve
the elliptic instability for the inviscid case. However, the model shifts the
critical stability angle. This shift increases (resp. decreases) the maximum
growth rate for long (resp. short) waves. It also introduces a band of stable
CC solutions for short waves.


title: Mechanism for the Intermittent Route to Strange Nonchaotic Attractors

abstract:
  Intermittent strange nonchaotic attractors (SNAs) appear typically in
quasiperiodically forced period-doubling systems. As a representative model, we
consider the quasiperiodically forced logistic map and investigate the
mechanism for the intermittent route to SNAs using rational approximations to
the quasiperiodic forcing. It is thus found that a smooth torus is transformed
into an intermittent SNA via a phase-dependent saddle-node bifurcation when it
collides with a new type of ``ring-shaped'' unstable set. Besides this
intermittent transition, other transitions such as the interior, boundary, and
band-merging crises may also occur through collision with the ring-shaped
unstable sets. Hence the ring-shaped unstable sets play a central role for such
dynamical transitions. Furthermore, these kinds of dynamical transitions seem
to be ``universal,'' in the sense that they occur typically in a large class of
quasiperiodically forced period-doubling systems.


title:
Nonlinear dynamics of waves and modulated waves in 1D thermocapillary
  flows. I: General presentation and periodic solutions

abstract:
  We present experimental results on hydrothermal traveling-waves dynamics in
long and narrow 1D channels. The onset of primary traveling-wave patterns is
briefly presented for different fluid heights and for annular or bounded
channels, i.e., within periodic or non-periodic boundary conditions. For
periodic boundary conditions, by increasing the control parameter or changing
the discrete mean-wavenumber of the waves, we produce modulated waves patterns.
These patterns range from stable periodic phase-solutions, due to supercritical
Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes
and/or counter-propagating-waves competition, i.e., traveling sources and
sinks. The transition from non-linearly saturated Eckhaus modulations to
transient pattern-breaks by traveling holes and spatio-temporal defects is
documented. Our observations are presented in the framework of coupled complex
Ginzburg-Landau equations with additional fourth and fifth order terms which
account for the reflection symmetry breaking at high wave-amplitude far from
onset. The second part of this paper (nlin.PS/0208030) extends this study to
spatially non-periodic patterns observed in both annular and bounded channel.


title:
Nonlinear dynamics of waves and modulated waves in 1D thermocapillary
  flows. II: Convective/absolute transitions

abstract:
  We present experimental results on hydrothermal waves in long and narrow 1D
channels. In a bounded channel, we describe the primary and secondary
instabilities leading to waves and modulated waves in terms of
convective/absolute transitions. Because of on the combined effect of finite
group velocity and of the presence of boundaries, the wave-patterns are
non-uniform in space. We also investigate non-uniform wave-patterns observed in
an annular channel in the presence of sources and sinks of hydrothermal waves.
We connect our observations with the complex Ginzburg-Landau model equation in
the very same way as in the first part of the paper (nlin.PS/0208029).


title:
Comment on: ``Semiclassical theory of spin-orbit interactions using spin
  coherent states''

abstract:
  We point out that a certain kind of combined classical translational and spin
dynamics -- claimed in [M. Pletyukhov, et al. Phys. Rev. Lett. 89 (2002)
116601] to arise from the Pauli equation in the semiclassical limit $\hbar\to0$
for fixed spin -- only shows up if one simultaneously considers the high spin
limit $S\to\infty$.


title:
Hamiltonian fractals and chaotic scattering of passive particles by a
  topographical vortex and an alternating current

abstract:
  We investigate the dynamics of passive particles in a two-dimensional
incompressible open flow composed of a fixed topographical point vortex and a
background current with a periodic component. The tracer dynamics is found to
be typically chaotic in a mixing region and regular in far upstream and
downstream regions of the flow. Chaotic advection of tracers is proven to be of
a homoclinic nature with transversal intersections of stable and unstable
manifolds of the saddle point. In spite of simplicity of the flow, chaotic
trajectories are very complicated alternatively sticking nearby boundaries of
the vortex core and islands of regular motion and wandering in the mixing
region. The boundaries act as dynamical traps for advected particles with a
broad distribution of trapping times. This implies the appearance of
fractal-like scattering function: dependence of the trapping time on initial
positions of the tracers. It is confirmed numerically by computing a trapping
map and trapping time distribution which is found to be initially Poissonian
with a crossover to a power law at the PDF tail. The mechanism of generating
the fractal is shown to resemble that of the Cantor set with the Hausdorff
fractal dimension of the scattering function to be equal to d ~= 1.84.


title: A New Test for Chaos

abstract:
  We describe a new test for determining whether a given deterministic
dynamical system is chaotic or nonchaotic. (This is an alternative to the usual
approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test
for chaos (the output is a 0 signifying nonchaotic or a 1 signifying chaotic)
and is independent of the dimension of the dynamical system. Moreover, the
underlying equations need not be known. The test works equally well for
continuous and discrete time. We give examples for an ordinary differential
equation, a partial differential equation and for a map.


title: Action Correlations and Random Matrix Theory

abstract:
  The correlations in the spectra of quantum systems are intimately related to
correlations which are of genuine classical origin, and which appear in the
spectra of actions of the classical periodic orbits of the corresponding
classical systems. We review this duality and the semiclassical theory which
brings it about. The conjecture that the quantum spectral statistics are
described in terms of Random Matrix Theory, leads to the proposition that the
classical two-point correlation function is given also in terms of a universal
function. We study in detail the spectrum of actions of the Baker map, and use
it to illustrate the steps needed to reveal the classical correlations, their
origin and their relation to symbolic dynamics.


title: Explicit Free Parameterization of the Modified Tetrahedron Equation

abstract:
  The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.


title: Discrete gap solitons in modulated waveguide arrays

abstract:
  We suggest a novel concept of diffraction management in waveguide arrays and
predict the existence of discrete gap solitons that possess the properties of
both conventional discrete and Bragg grating solitons. We demonstrate that both
the soliton velocity and propagation direction can be controlled by varying the
input light intensity.


title:
Fractal analysis on a closed classical hard-wall billiard using a
  simplified box-counting algorithm

abstract:
  We perform fractal analysis on a closed classical hard-wall billiard, the
circular billiard with a straight cut, assuming there are two openings on the
boundary. We use a two-dimensional set of initial conditions that produce all
possible trajectories of a particle injected from one opening, and numerically
compute the fractal dimension of singular points of a function that maps an
initial condition to the number of collisions with the wall before the exit. We
introduce a simplified box-counting algorithm, which uses points from a
rectangular grid inside the two-dimensional set of the initial conditions, to
simplify the calculation, and observe the classical chaotic properties while
varying the parameters of the billiard.


title: Ray stability in weakly range-dependent sound channels

abstract:
  Ray stability is investigated in environments consisting of a
range-independent background sound-speed profile on which a range-dependent
perturbation, such as that produced by internal waves in deep ocean
environments, is superimposed. Numerical results show that ray stability is
strongly influenced by the background sound speed profile. Ray instability is
shown to increase with increasing magnitude of alpha := I omega^{prime} /
omega, where 2 pi / omega(I) is the range of a ray double loop and I is the ray
action variable. The mechanism, shear-induced instability enhancement, by which
alpha controls ray instability is described.


title: Effects of RF Stimulus and Negative Feedback on Nonlinear Circuits

abstract:
  We investigate the combined effect of rectification and nonlinear dynamics on
the behavior of several simple nonlinear circuits. We consider the classic
Resistor-Inductor-Diode (RLD) circuit driven by a low frequency source when an
operational amplifier with negative feedback is added to the circuit. Radio
frequency signals are applied to the circuit, causing significant changes in
the onset of period-doubling and chaos. Measurements indicate that this effect
is associated with a DC voltage induced by rectification of the RF signal in
the circuit. The combination of rectification and nonlinear circuit dynamics
produce qualitatively new behavior, which opens up a new channel of RF
interference in circuits.


title:
Synchronizing to Periodicity: The Transient Information and
  Synchronization Time of Periodic Sequences

abstract:
  We analyze how difficult it is to synchronize to a periodic sequence whose
structure is known, when an observer is initially unaware of the sequence's
phase. We examine the transient information T, a recently introduced
information-theoretic quantity that measures the uncertainty an observer
experiences while synchronizing to a sequence. We also consider the
synchronization time tau, which is the average number of measurements required
to infer the phase of a periodic signal. We calculate T and tau for all
periodic sequences up to and including period 23. We show which sequences of a
given period have the maximum and minimum possible T and tau values, develop
analytic expressions for the extreme values, and show that in these cases the
transient information is the product of the total phase information and the
synchronization time. Despite the latter result, our analyses demonstrate that
the transient information and synchronization time capture different and
complementary structural properties of individual periodic sequences --
properties, moreover, that are distinct from source entropy rate and mutual
information measures, such as the excess entropy.


title: Interaction of vector solitons with a nonlinear interface

abstract:
  We develop the analytical method of field momenta for analyzing the dynamics
of optical vector solitons in photorefractive nonlinear media. First, we derive
the effective evolution equations for the parameters of multi-component
solitons composed of incoherently coupled beams and investigate the soliton
internal oscillations associated with the relative motion of the soliton
components. Then, we apply this method for analyzing the vector soliton
scattering by a nonlinear interface. In particular, we show that a vector
soliton can be reflected, transmitted, captured, or split into separate
components, depending on the initial energy of its internal degree of freedom.
The results are verified by direct numerical simulations of spatial optical
solitons in photorefractive nonlinear media.


title: Fundamental Cycle of a Periodic Box-Ball System

abstract:
  We investigate a soliton cellular automaton (Box-Ball system) with periodic
boundary conditions. Since the cellular automaton is a deterministic dynamical
system that takes only a finite number of states, it will exhibit periodic
motion. We determine its fundamental cycle for a given initial state.


title: Soliton X-junctions with controllable transmission

abstract:
  We propose new planar X-junctions and multi-port devices written by spatial
solitons, which are composed of two (or more) nonlinearly coupled components in
Kerr-type media. Such devices have no radiation losses at a given wavelength.
We demonstrate that, for the same relative angle between the channels of the
X-junctions, one can vary the transmission coefficients into the output
channels by adjusting the polarizations of multi-component solitons. We
determine analytically the transmission properties and suggest two types of
experimental embodiments of the proposed device.


title: Short time decay of the Loschmidt echo

abstract:
  The Loschmidt echo measures the sensitivity to perturbations of quantum
evolutions. We study its short time decay in classically chaotic systems. Using
perturbation theory and throwing out all correlation imposed by the initial
state and the perturbation, we show that the characteristic time of this regime
is well described by the inverse of the width of the local density of states.
This result is illustrated and discussed in a numerical study in a
2-dimensional chaotic billiard system perturbed by various contour deformations
and using different types of initial conditions. Moreover, the influence to the
short time decay of sub-Planck structures developed by time evolution is also
investigated.


title: Polychromatic solitons in a quadratic medium

abstract:
  We introduce the simplest model to describe parametric interactions in a
quadratically nonlinear optical medium with the fundamental harmonic containing
two components with (slightly) different carrier frequencies [which is a direct
analog of wavelength-division multiplexed (WDM) models, well known in media
with cubic nonlinearity]. The model takes a closed form with three different
second-harmonic components, and it is formulated in the spatial domain. We
demonstrate that the model supports both polychromatic solitons (PCSs), with
all the components present in them, and two types of mutually orthogonal simple
solitons, both types being stable in a broad parametric region. An essential
peculiarity of PCS is that its power is much smaller than that of a simple
(usual) soliton (taken at the same values of control parameters), which may be
an advantage for experimental generation of PCSs. Collisions between the
orthogonal simple solitons are simulated in detail, leading to the conclusion
that the collisions are strongly inelastic, converting the simple solitons into
polychromatic ones, and generating one or two additional PCSs. A collision
velocity at which the inelastic effects are strongest is identified, and it is
demonstrated that the collision may be used as a basis to design a simple
all-optical XOR logic gate.


title:
Transverse instability and its long-term development for solitary waves
  of the (2+1)-Boussinesq equation

abstract:
  The stability properties of line solitary wave solutions of the
(2+1)-dimensional Boussinesq equation with respect to transverse perturbations
and their consequences are considered. A geometric condition arising from a
multi-symplectic formulation of this equation gives an explicit relation
between the parameters for transverse instability when the transverse
wavenumber is small. The Evans function is then computed explicitly, giving the
eigenvalues for transverse instability for all transverse wavenumbers. To
determine the nonlinear and long time implications of transverse instability,
numerical simulations are performed using pseudospectral discretization. The
numerics confirm the analytic results, and in all cases studied, transverse
instability leads to collapse.


title:
Semiclassical spin coherent state method in the weak spin-orbit coupling
  limit

abstract:
  We apply the semiclassical spin coherent state method for the density of
states by Pletyukhov et al. (2002) in the weak spin-orbit coupling limit and
recover the modulation factor in the semiclassical trace formula found by Bolte
and Keppeler (1998, 1999).


title: The entropy of 'strange' billiards inside n-simplexes

abstract:
  In the present work we investigate a new type of billiards defined inside
n-simplex regions. We determine an invariant ergodic (SRB) measure of the
dynamics for any dimension. In using symbolic dynamics the (KS or metric)
entropy is computed and we find that the system is chaotic for all cases n > 2.

categories: nlin.CD cond-mat.stat-mech math-ph math.DS math.MP physics.data-an


title:
Discrete kink dynamics in hydrogen-bonded chains I: The one-component
  model

abstract:
  We study topological solitary waves (kinks and antikinks) in a nonlinear
one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse
type. This chain is used to describe the collective proton dynamics in
quasi-one-dimensional networks of hydrogen bonds, where the on-site potential
plays role of the proton potential in the hydrogen bond. The system supports a
rich variety of stationary kink solutions with different symmetry properties.
We study the stability and bifurcation structure of all these stationary kink
states. An exactly solvable model with a piecewise ``parabola-constant''
approximation of the double-Morse potential is suggested and studied
analytically. The dependence of the Peierls-Nabarro potential on the system
parameters is studied. Discrete travelling-wave solutions of a narrow permanent
profile are shown to exist, depending on the anharmonicity of the Morse
potential and the cooperativity of the hydrogen bond (the coupling constant of
the interaction between nearest-neighbor protons).


title: Uniform semiclassical wave function for coherent 2D electron flow

abstract:
  We find a uniform semiclassical (SC) wave function describing coherent
branched flow through a two-dimensional electron gas (2DEG), a phenomenon
recently discovered by direct imaging of the current using scanned probed
microscopy. The formation of branches has been explained by classical
arguments, but the SC simulations necessary to account for the coherence are
made difficult by the proliferation of catastrophes in the phase space. In this
paper, expansion in terms of "replacement manifolds" is used to find a uniform
SC wave function for a cusp singularity. The method is then generalized and
applied to calculate uniform wave functions for a quantum-map model of coherent
flow through a 2DEG. Finally, the quantum-map approximation is dropped and the
method is shown to work for a continuous-time model as well.


title: A discrete nonlinear model with substrate feedback

abstract:
  We consider a prototypical model in which a nonlinear field (continuum or
discrete) evolves on a flexible substrate which feeds back to the evolution of
the main field. We identify the underlying physics and potential applications
of such a model and examine its simplest one-dimensional Hamiltonian form,
which turns out to be a modified Frenkel-Kontorova model coupled to an extra
linear equation. We find static kink solutions and study their stability, and
then examine moving kinks (the continuum limit of the model is studied too). We
observe how the substrate effectively renormalizes properties of the kinks. In
particular, a nontrivial finding is that branches of stable and unstable kink
solutions may be extended beyond a critical point at which an effective
intersite coupling vanishes; passing this critical point does not destabilize
the kink. Kink-antikink collisions are also studied, demonstrating alternation
between merger and transmission cases.


title:
Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de
  Vries equations

abstract:
  Periodic waves are investigated in a system composed of a
Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly
coupled to an extra linear dissipative equation. The model describes, e.g., a
two-layer liquid film flowing down an inclined plane. It has been recently
shown that the system supports stable solitary pulses. We demonstrate that a
perturbation analysis, based on the balance equation for the field momentum,
predicts the existence of stable cnoidal waves (CnWs) in the same system. It is
found that the mean value U of the wave field u in the main subsystem, but not
the mean value of the extra field, affects the stability of the periodic waves.
Three different areas can be distinguished inside the stability region in the
parameter plane (L,U), where L is the wave's period. In these areas, stable
are, respectively, CnWs with positive velocity, constant solutions, and CnWs
with negative velocity. Multistability, i.e., the coexistence of several
attractors, including the waves with several maxima per period, appears at
large value of L. The analytical predictions are completely confirmed by direct
simulations. Stable waves are also found numerically in the limit of vanishing
dispersion, when the KS-KdV equation goes over into the KS one.


title:
Spontaneously appearing diskrete moving kinks in nonlinear acoustic
  chain with realistic potentials

abstract:
  Molecular dynamic simulations are performed to investigate a long-time
evolution of different type initial signals in nonlinear acoustic chains with
realistic Exp-6 potential and with power ones. Finite number of long-lifetime
kink-shaped excitations is observed in the system in thermodynamic equilibrium.
Dynamical equilibrium between the processes of their growth and decay is found.


title: Analytic Proof of the Attractors of a Class of Cellular Automaton

abstract:
  In this work we provide analytic results of infinite one-dimensional cellular
automaton(CA). By realizing symbolic products, we investigate a subclass of
infinite CA and prove analytically that within this subclass the only allowed
attractors are homogenous, steady and periodic states for arbitrary initial
configuration. Our method also provide exact enumeration of these attractors
and it is shown explicitly in a particular model.


title:
Nonlinear Behavior in Ferromagnetism: Simple Example and Possible
  Implications

abstract:
  Two cases of a phenomenological model for ferromagnetism are considered,
discrete and continuous. And the relationship, in general, between discrete and
continuous models explored. In a similar way to the logistic map behavior, the
continuous case is exactly solvable while the discrete one contains the
bifurcation route to chaos. Through the ferromagnetic interpretation I comment
on the relevance of this to understanding evolution of systems in time, the
role of the configuration space in chaotic behavior, and how this understanding
may lead to new exotic magnetic phenomena.


title:
On the non-integrability of a fifth order equation with integrable
  two-body dynamics

abstract:
  We consider the fifth order partial differential equation (PDE)
$u_{4x,t}-5u_{xxt}+4u_t+uu_{5x}+2u_xu_{4x}-5uu_{3x}-10u_xu_{xx}+12uu_x=0$,
which is a generalization of the integrable Camassa-Holm equation. The fifth
order PDE has exact solutions in terms of an arbitrary number of superposed
pulsons, with geodesic Hamiltonian dynamics that is known to be integrable in
the two-body case N=2. Numerical simulations show that the pulsons are stable,
dominate the initial value problem and scatter elastically. These
characteristics are reminiscent of solitons in integrable systems. However,
after demonstrating the non-existence of a suitable Lagrangian or
bi-Hamiltonian structure, and obtaining negative results from Painlev\'{e}
analysis and the Wahlquist-Estabrook method, we assert that the fifth order PDE
is not integrable.


title: Integrable and non-integrable equations with peakons

abstract:
  We consider a one-parameter family of non-evolutionary partial differential
equations which includes the integrable Camassa-Holm equation and a new
equation first isolated by Degasperis and Procesi. A Lagrangian and Hamiltonian
formulation is presented for the whole family of equations, and we discuss how
this fits into a bi-Hamiltonian framework in the integrable cases. The
Hamiltonian dynamics of peakons and some other special finite-dimensional
reductions are also described.


title: Wave chaos in the elastic disc

abstract:
  The relation between the elastic wave equation for plane, isotropic bodies
and an underlying classical ray dynamics is investigated. We study in
particular the eigenfrequencies of an elastic disc with free boundaries and
their connection to periodic rays inside the circular domain. Even though the
problem is separable, wave mixing between the shear and pressure component of
the wave field at the boundary leads to an effective stochastic part in the ray
dynamics. This introduces phenomena typically associated with classical chaos
as for example an exponential increase in the number of periodic orbits.
Classically, the problem can be decomposed into an integrable part and a simple
binary Markov process. Similarly, the wave equation can in the high frequency
limit be mapped onto a quantum graph. Implications of this result for the level
statistics are discussed. Furthermore, a periodic trace formula is derived from
the scattering matrix based on the inside-outside duality between eigen-modes
and scattering solutions and periodic orbits are identified by Fourier
transforming the spectral density


title:
Implications of Correlated Default For Portfolio Allocation To Corporate
  Bonds

abstract:
  This article deals with the problem of optimal allocation of capital to
corporate bonds in fixed income portfolios when there is the possibility of
correlated defaults. Using a multivariate normal Copula function for the joint
default probabilities we show that retaining the first few moments of the
portfolio default loss distribution gives an extremely good approximation to
the full solution of the asset allocation problem. We provide detailed results
on the convergence of the moment expansion and explore how the optimal
portfolio allocation depends on recovery fractions, level of diversification
and investment time horizon. Numerous numerical illustrations exhibit the
results for simple portfolios and utility functions.


title:
Spatial representation of temporal information through spike timing
  dependent plasticity

abstract:
  We suggest a mechanism based on spike time dependent plasticity (STDP) of
synapses to store, retrieve and predict temporal sequences. The mechanism is
demonstrated in a model system of simplified integrate-and-fire type neurons
densely connected by STDP synapses. All synapses are modified according to the
so-called normal STDP rule observed in various real biological synapses. After
conditioning through repeated input of a limited number of of temporal
sequences the system is able to complete the temporal sequence upon receiving
the input of a fraction of them. This is an example of effective unsupervised
learning in an biologically realistic system. We investigate the dependence of
learning success on entrainment time, system size and presence of noise.
Possible applications include learning of motor sequences, recognition and
prediction of temporal sensory information in the visual as well as the
auditory system and late processing in the olfactory system of insects.

categories: nlin.AO cond-mat.dis-nn physics.bio-ph q-bio.NC


title: Non-trivial class of the mixed U(\sigma+\mu)-vector solitons

abstract:
  There has been found an exact solution of the mixed problem for Shrodinger's
compact U(m)-vector nonlinear model with an arbitrary sign of the coupling
constant. It is shown, that in case of m>2 there is a new class of solutions -
mixed U(\sigma+\mu)-vector solitons with "inelastic" (changing the form without
the energy loss) interaction at \sigma>1 and strict elastic - at \sigma=1. They
correspond to the color complexes consisting of \sigma-bright and \mu-dark
solitons (\sigma+\mu=m) and they can exist both in self-focusing and defocusing
medias. The universal N-soliton formula for the attraction and repulsion cases
has been obtained by the method of Hirota for the first time.


title: Decay of scalar turbulence revisited

abstract:
  We demonstrate that at long times the rate of passive scalar decay in a
turbulent, or simply chaotic, flow is dominated by regions (in real space or in
inverse space) where mixing is less efficient. We examine two situations. The
first is of a spatially homogeneous stationary turbulent flow with both viscous
and inertial scales present. It is shown that at large times scalar
fluctuations decay algebraically in time at all spatial scales (particularly in
the viscous range, where the velocity is smooth). The second example explains
chaotic stationary flow in a disk/pipe. The boundary region of the flow
controls the long-time decay, which is algebraic at some transient times, but
becomes exponential, with the decay rate dependent on the scalar diffusion
coefficient, at longer times.


title:
Separable Hamiltonian equations on Riemann manifolds and related
  integrable hydrodynamic systems

abstract:
  A systematic construction of St\"{a}ckel systems in separated coordinates and
its relation to bi-Hamiltonian formalism are considered. A general form of
related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is
derived. One Casimir bi-Hamiltonian case is studed in details and in this case,
a systematic construction of related hydrodynamic systems in arbitrary
coordinates is presented, using a cofactor method and soliton symmetry
constraints.


title: Time-frequency analysis of chaotic systems

abstract:
  We describe a method for analyzing the phase space structures of Hamiltonian
systems. This method is based on a time-frequency decomposition of a trajectory
using wavelets. The ridges of the time-frequency landscape of a trajectory,
also called instantaneous frequencies, enable us to analyze the phase space
structures. In particular, this method detects resonance trappings and
transitions and allows a characterization of the notion of weak and strong
chaos. We illustrate the method with the trajectories of the standard map and
the hydrogen atom in crossed magnetic and elliptically polarized microwave
fields.


title:
Leading off-diagonal approximation for the spectral form factor for
  uniformly hyperbolic systems

abstract:
  We consider the semiclassical approximation to the spectral form factor
K(tau) for two-dimensional uniformly hyperbolic systems, and derive the first
off-diagonal correction for small tau. The result agrees with the tau^2-term of
the form factor for the GOE random matrix ensemble.


title: Solitons in coupled Ablowitz-Ladik chains

abstract:
  A model of two coupled Ablowitz-Ladik (AL) lattices is introduced. While the
system as a whole is not integrable, it admits reduction to the integrable AL
model for symmetric states. Stability and evolution of symmetric solitons are
studied in detail analytically (by means of a variational approximation) and
numerically. It is found that there exists a finite interval of positive values
of the coupling constant in which the symmetric soliton is stable, provided
that its mass is below a threshold value. Evolution of the unstable symmetric
soliton is further studied by means of direct simulations. It is found that the
unstable soliton breaks up and decays into radiation, or splits into two
counter-propagating asymmetric solitons, or evolves into an asymmetric pulse,
depending on the coupling coefficient and the mass of the initial soliton.


title: Parasupersymmetric structure of the Boussinesq-type systems

abstract:
  We study Darboux transformations for a Boussinesq-type equations. The
parasupersymmetric structure of link between Boussinesq and modified Boussinesq
systems is revealed.


title:
Spectral curves and parameterizations of a discrete integrable
  3-dimensional model

abstract:
  We consider a discrete classical integrable model on the 3-dimensional cubic
lattice. The solutions of this model can be used to parameterize the Boltzmann
weights of the different 3-dimensional spin models. We have found the general
solution of this model constructed in terms of the theta-functions defined on
an arbitrary compact algebraic curve. The imposing of the periodic boundary
conditions fixes the algebraic curve. We have shown that in this case the curve
coincides with the spectral one of the auxiliary linear problem. In the case
when the curve is a rational one, the soliton solutions have been constructed.


title: Energy transmission in the forbidden bandgap of a nonlinear chain

abstract:
  A nonlinear chain driven by one end may propagate energy in the forbidden
band gap by means of nonlinear modes. For harmonic driving at a given
frequency, the process ocurs at a threshold amplitude by sudden large energy
flow, that we call nonlinear supratransmission. The bifurcation of energy
transmission is demonstrated numerically and experimentally on the chain of
coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and
sustained by an extremely simple theory.


title:
Integrable hierarchy, $3\times 3$ constrained systems, and parametric
  and peaked stationary solutions

abstract:
  This paper gives a new integrable hierarchy of nonlinear evolution equations.
The DP equation: $m_t+um_x+3mu_x=0, m=u-u_{xx}$, proposed recently by
Desgaperis and Procesi \cite{DP[1999]}, is the first one in the negative
hierarchy while the first one in the positive hierarchy is:\
$m_t=4(m^{-{2/3}})_x-5(m^{-{2/3}})_{xxx}+ (m^{-{2/3}})_{xxxxx}$. The whole
hierarchy is shown Lax-integrable through solving a key matrix equation. To
obtain the parametric solutions for the whole hierarchy, we separatedly discuss
the negative and the positive hierarchies. For the negative hierarchy, its
$3\times3$ Lax pairs and corresponding adjoint representations are
nonlinearized to be Liouville-integrable Hamiltonian canonical systems under
the so-called Dirac-Poisson bracket defined on a symplectic submanifold of
$\R^{6N} $. Based on the integrability of those finite-dimensional canonical
Hamiltonian systems we give the parametric solutions of the all equations in
the negative hierarchy. In particular, we obtain the parametric solution of the
DP equation. Moreover, for the positive hierarchy, we consider the different
constraint and use a similar procudure to the negative case to obtain the
parametric solutions of the positive hierarchy. In particular, we give the
parametric solution of the 5th-order PDE
$m_t=4(m^{-{2/3}})_x-5(m^{-{2/3}})_{xxx}+ (m^{-{2/3}})_{xxxxx}$. Finally, we
discuss the stationary solutions of the 5th-order PDE, and particularly give
its four peaked stationary solutions. The stationary solutions may be included
in the parametric solution, but the peaked stationary solutions not. The
5th-order PDE does not have the cusp soliton although it looks like a higher
order Harry-Dym equation.


title:
Semi-stability of embedded solitons in the general fifth-order KdV
  equation

abstract:
  Evolution of perturbed embedded solitons in the general Hamiltonian
fifth-order Korteweg--de Vries (KdV) equation is studied. When an embedded
soliton is perturbed, it sheds a one-directional continuous-wave radiation. It
is shown that the radiation amplitude is not minimal in general. A dynamical
equation for velocity of the perturbed embedded soliton is derived. This
equation shows that a neutrally stable embedded soliton is in fact semi-stable.
When the perturbation increases the momentum of the embedded soliton, the
perturbed state approaches asymptotically the embedded soliton, while when the
perturbation reduces the momentum of the embedded soliton, the perturbed state
decays into radiation. Classes of initial conditions to induce soliton decay or
persistence are also determined. Our analytical results are confirmed by direct
numerical simulations of the fifth-order KdV equation.


title:
A new class of scale free solutions to linear ordinary differential
  equations and the universality of the Golden Mean ${\frac{\sqrt{5}-1}{2}}$}

abstract:
  A new class of finitely differentiable scale free solutions to the simplest
class of ordinary differential equations is presented. Consequently, the real
number set gets replaced by an extended physical set, each element of which is
endowed with an equivalence class of infinitesimally separated neighbours in
the form of random fluctuations. We show how a sense of time and evolution is
intrinsically defined by the infinite continued fraction of the golden mean
irrational number ${\frac{\sqrt{5}-1}{2}}$, which plays a key role in this
extended SL(2,R) formalism of Calculus. Time may thereby undergo random
inversions generating well defined random scales, thus allowing a dynamical
system to evolve self similarly over the set of multiple scales. The late time
stochastic fluctuations of a dynamical system enjoys the generic $1/f$
spectrum. A universal form of the related probability density is also derived.
We prove that the golden mean number is intrinsically random, letting all
measurements in the physical universe fundamentally uncertain. The present
analysis offers an explanation of the universal occurrence of the golden mean
in diverse natural and biological processes.


title: Excitable media in open and closed chaotic flows

abstract:
  We investigate the response of an excitable medium to a localized
perturbation in the presence of a two-dimensional smooth chaotic flow. Two
distinct types of flows are numerically considered: open and closed. For both
of them three distinct regimes are found, depending on the relative strengths
of the stirring and the rate of the excitable reaction. In order to clarify and
understand the role of the many competing mechanisms present, simplified models
of the process are introduced. They are one-dimensional baker-map models for
the flow and a one-dimensional approximation for the transverse profile of the
filaments.


title:
A scalar nonlocal bifurcation of solitary waves for coupled nonlinear
  Schroedinger systems

abstract:
  An explanation is given for previous numerical results which suggest a
certain bifurcation of `vector solitons' from scalar (single-component)
solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation
in question is nonlocal in the sense that the vector soliton does not have a
small-amplitude component, but instead approaches a solitary wave of one
component with two infinitely far-separated waves in the other component. Yet,
it is argued that this highly nonlocal event can be predicted from a purely
local analysis of the central solitary wave alone. Specifically the
linearisation around the central wave should contain asymptotics which grow at
precisely the speed of the other-component solitary waves on the two wings.
This approximate argument is supported by both a detailed analysis based on
matched asymptotic expansions, and numerical experiments on two example
systems. The first is the usual coupled NLS system involving an arbitrary ratio
between the self-phase and cross-phase modulation terms, and the second is a
coupled NLS system with saturable nonlinearity that has recently been
demonstrated to support stable multi-peaked solitary waves. The asymptotic
analysis further reveals that when the curves which define the proposed
criterion for scalar nonlocal bifurcations intersect with boundaries of certain
local bifurcations, the nonlocal bifurcation could turn from scalar to
non-scalar at the intersection. This phenomenon is observed in the first
example. Lastly, we have also selectively tested the linear stability of
several solitary waves just born out of scalar nonlocal bifurcations. We found
that they are linearly unstable. However, they can lead to stable solitary
waves through parameter continuation.


title: An integrable hierarchy, parametric solution and traveling wave solution

abstract:
  This paper gives an integrable hierarchy of nonlinear evolution equations. In
this hierarchy there are the following representative equations: \beqq & &
u_t=\pa^5_x u^{-{2/3}}, & & u_t=\pa^5_x\frac{(u^{-{1/3}})_{xx}
  -2(u^{-{1/6}})_{x}^2}{u}; & & u_{xxt}+3u_{xx}u_x+u_{xxx}u=0. \eeqq The first
two are in the positive order hierarchy while the 3rd one is in the negative
order hierarchy. The whole hierarchy is shown integrable through solving a key
$3\times 3 $ matrix equation. The $3\times3$ Lax pairs and their adjoint
representations are nonlinearized to be two Liouville-integrable canonical
Hamiltonian systems. Based on the integrability of $6N$-dimensional systems we
give the parametric solution of the positive hierarchy. In particular, we
obtain the parametric solution of the equation $u_t=\pa^5_x u^{-{2/3}}$.
Moreover, we give the traveling wave solution (TWS) of the above three
equations. The TWSs of the first two equations have singularity and look like
cusp (cusp-like), but the TWS of the 3rd one is continuous. For the 5th-order
equation, its parametric solution can not include its singular TWS. We also
analyse the Gaussian initial solutions for the equations $u_t=\pa^5_x
u^{-{2/3}}$, and $u_{xxt}+3u_{xx}u_x+u_{xxx}u=0.$ One is stable, the other not.
Finally, we extend the equation $u_t=\pa^5_x u^{-{2/3}}$ to a large class of
equations $ u_t=\partial_x^l u^{-m/n}, l\ge1, n\not=0, m,n \in \Z, $ which
still have the singular cusp-like traveling wave solutions.


title: Ladder Operators for Integrable One-Dimensional Lattice Models

abstract:
  A generalised ladder operator is used to construct the conserved operators
for any model derived from the Yang-Baxter equation. As an example, the low
order conserved operators for the XYh model are calculated explicitly.


title:
Reply to a Comment by J. Bolte, R. Glaser and S. Keppeler on:
  Semiclassical theory of spin-orbit interactions using spin coherent states

abstract:
  We reply to a Comment on our recently proposed semiclassical theory for
systems with spin-orbit interactions.


title: Jets, Stickiness and Anomalous Transport

abstract:
  Dynamical and statistical properties of the vortex and passive particle
advection in chaotic flows generated by four and sixteen point vortices are
investigated. General transport properties of these flows are found anomalous
and exhibit a superdiffusive behavior with typical second moment exponent (\mu
\sim 1.75). The origin of this anomaly is traced back to the presence of
coherent structures within the flow, the vortex cores and the region far from
where vortices are located. In the vicinity of these regions stickiness is
observed and the motion of tracers is quasi-ballistic. The chaotic nature of
the underlying flow dictates the choice for thorough analysis of transport
properties. Passive tracer motion is analyzed by measuring the mutual relative
evolution of two nearby tracers. Some tracers travel in each other vicinity for
relatively large times. This is related to an hidden order for the tracers
which we call jets. Jets are localized and found in sticky regions. Their
structure is analyzed and found to be formed of a nested sets of jets within
jets. The analysis of the jet trapping time statistics shows a quantitative
agreement with the observed transport exponent.


title: Tau-functions and special solutions in a coupled Painlev\'e system

abstract:
  For a pair of coupled Painlev\'e equations obtained as a similarity reduction
of the Hirota-Satsuma systems we describe special parameter-families of
solutions given in terms of mixtures of rational and Airy functions, and in
terms of a second Painlev\'e transcendent. The tau-functions associated to some
of these solutions are also given explicitly.


title: Relaxation and Diffusion in a Globally Coupled Hamiltonian System

abstract:
  The relation between relaxation and diffusion is investigated in a
Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and
only if the system is going towards equilibrium. The anomaly in diffusion is
not anomalous diffusion taking a power-type function, but is a transient
anomaly due to non-stationarity. Contrary to previous claims, in
quasi-stationary states, diffusion can be explained by a stretched exponential
correlation function, whose stretching exponent is almost constant and
correlation time is linear as functions of degrees of freedom. The full time
evolution is characterized by varying stretching exponent and correlation time.


title:
Superiority of semiclassical over quantum mechanical calculations for a
  three-dimensional system

abstract:
  In systems with few degrees of freedom modern quantum calculations are, in
general, numerically more efficient than semiclassical methods. However, this
situation can be reversed with increasing dimension of the problem. For a
three-dimensional system, viz. the hyperbolic four-sphere scattering system, we
demonstrate the superiority of semiclassical versus quantum calculations.
Semiclassical resonances can easily be obtained even in energy regions which
are unattainable with the currently available quantum techniques.


title:
Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of
  Two or More Dimensions

abstract:
  We consider the existence of robust strange nonchaotic attractors (SNA's) in
a simple class of quasiperiodically forced systems. Rigorous results are
presented demonstrating that the resulting attractors are strange in the sense
that their box-counting dimension is N+1 while their information dimension is
N. We also show how these properties are manifested in numerical experiments.