title: Birkhoff normal form for the periodic Toda lattice

abstract:
  In this paper we compute the Birkhoff normal form of the periodic Toda
lattice up to order four. As an application, we verify that Kolmogorov's
nondegeneracy condition in the KAM theorem holds almost everywhere in phase
space.


title:
Hypothesis of strong chaos and anomalous diffusion in coupled symplectic
  maps

abstract:
  We investigate the high dimensional Hamiltonian chaotic dynamics in $N$
coupled area-preserving maps. We show the existence of an enhanced trapping
regime caused by trajectories performing a random walk {\em inside} the area
corresponding to regular islands of the uncoupled maps. As a consequence, we
observe long intermediate regimes of power-law decay of the recurrence time
statistics (with exponent $\gamma=0.5$) and of ballistic motion. The asymptotic
decay of correlations and anomalous diffusion depend on the stickiness of the
$N$-dimensional invariant tori. Detailed numerical simulations show weaker
stickiness for increasing $N$ suggesting that high-dimensional Hamiltonian
systems asymptotically fulfill the demands of the usual hypotheses of strong
chaos.


title: Complete chaotic synchronization in mutually coupled time-delay systems

abstract:
  Complete chaotic synchronization of end lasers has been observed in a line of
mutually coupled, time-delayed system of three lasers, with no direct
communication between the end lasers. The present paper uses ideas from
generalized synchronization to explain the complete synchronization in the
presence of long coupling delays, applied to a model of mutually coupled
semiconductor lasers in a line. These ideas significantly simplify the analysis
by casting the stability in terms of the local dynamics of each laser. The
variational equations near the synchronization manifold are analyzed, and used
to derive the synchronization condition that is a function of the parameters.
The results explain and predict the dependence of synchronization on various
parameters, such as time-delays, strength of coupling and dissipation. The
ideas can be applied to understand complete synchronization in other chaotic
systems with coupling delays and no direct communication between synchronized
sub-systems.


title: Embedded solitons in the third-order nonlinear Schr\"{o}dinger equation

abstract:
  We derive a straightforward variational method to construct embedded soliton
solutions of the third-order nonlinear Sch\"odinger equation and analytically
demonstrate that these solitons exist as a continuous family. We argue that a
particular embedded soliton when perturbed may always relax to the adjacent one
so as to make it fully stable.


title:
Memory difference control of unknown unstable fixed points: Drifting
  parameter conditions and delayed measurement

abstract:
  Difference control schemes for controlling unstable fixed points become
important if the exact position of the fixed point is unavailable or moving due
to drifting parameters. We propose a memory difference control method for
stabilization of a priori unknown unstable fixed points by introducing a memory
term. If the amplitude of the control applied in the previous time step is
added to the present control signal, fixed points with arbitrary Lyapunov
numbers can be controlled. This method is also extended to compensate arbitrary
time steps of measurement delay. We show that our method stabilizes orbits of
the Chua circuit where ordinary difference control fails.


title:
An envelope-function approach for a one-dimensional photonic crystal
  containing single negative materials

abstract:
  An envelope function approach is used to study the wave propagation in a
one-dimensional Photonic Crystal containing single negative layers. This
approach enables one to obtain the analytic expressions of the parameters of an
equivalent effective medium. From these parameters, it is seen that the
periodic structure appears to be an equivalent left-handed medium for the
envelope function. For the nonlinear wave propagation the phenomenon of
bistability and gap soliton formation near the edges of the zero-phi gap is
discussed.


title: Statistics of Entropy Production in Linearized Stochastic System

abstract:
  We consider a wide class of linear stochastic problems driven off the
equilibrium by a multiplicative asymmetric force. The force brakes detailed
balance, maintained otherwise, thus producing entropy. The large deviation
function of the entropy production in the system is calculated explicitly. The
general result is illustrated using an example of a polymer immersed in a
gradient flow and subject to thermal fluctuations.


title: Scaling properties of invariant densities of coupled Tchebyscheff maps

abstract:
  We study 1-dimensional coupled map lattices consisting of diffusively coupled
Tchebyscheff maps of N-th order. For small coupling constants a we determine
the invariant 1-point and 2-point densities of these nonhyperbolic systems in a
perturbative way. For arbitrarily small couplings a>0 the densities exhibit a
selfsimilar cascade of patterns, which we analyse in detail. We prove that
there are log-periodic oscillations of the density both in phase space as well
as in parameter space. We show that expectations of arbitrary observables scale
with \sqrt{a} in the low-coupling limit, contrasting the case of hyperbolic
maps where one has scaling with a. Moreover we prove that there are
log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence
of the expectation value of any given observable.


title:
Non-permanent form solutions in the Hamiltonian formulation of surface
  water waves

abstract:
  Using the KAM method, we exhibit some solutions of a finite-dimensional
approximation of the Zakharov Hamiltonian formulation of gravity water waves,
which are spatially periodic, quasi-periodic in time, and not permanent form
travelling waves. For this Hamiltonian, which is the total energy of the waves,
the canonical variables are some complex quantities an and a*n, which are
linear combinations of the Fourier components of the free surface elevation and
the velocity potential evaluated at the surface. We expose the method for the
case of a system with a finite number of degrees of freedom, the Zufiria model,
with only 3 modes interacting.


title:
Exact Solution of the Hyperbolic Generalization of Burgers Equation,
  Describing Travelling Fronts and their Interaction

abstract:
  We present new analytical solutions to the hyperbolic generalization of
Burgers equation, describing interaction of the wave fronts. To obtain them, we
employ a modified version of the Hirota method.


title: Dynamical Slowdown of Polymers in Laminar and Random Flows

abstract:
  The influence of an external flow on the relaxation dynamics of a single
polymer is investigated theoretically and numerically. We show that a
pronounced dynamical slowdown occurs in the vicinity of the coil-stretch
transition, especially when the dependence on polymer conformation of the drag
is accounted for. For the elongational flow, relaxation times are exceedingly
larger than the Zimm relaxation time, resulting in the observation of
conformation hysteresis. For random smooth flows hysteresis is not present.
Yet, relaxation dynamics is significantly slowed down because of the large
variety of accessible polymer configurations. The implications of these results
for the modeling of dilute polymer solutions in turbulent flows are addressed.


title: Refuting the odd number limitation of time-delayed feedback control

abstract:
  We refute an often invoked theorem which claims that a periodic orbit with an
odd number of real Floquet multipliers greater than unity can never be
stabilized by time-delayed feedback control in the form proposed by Pyragas.
Using a generic normal form, we demonstrate that the unstable periodic orbit
generated by a subcritical Hopf bifurcation, which has a single real unstable
Floquet multiplier, can in fact be stabilized. We derive explicit analytical
conditions for the control matrix in terms of the amplitude and the phase of
the feedback control gain, and present a numerical example. Our results are of
relevance for a wide range of systems in physics, chemistry, technology,and
life sciences, where subcritical Hopf bifurcations occur.


title: Hydrodynamical vortex on the plane

abstract:
  The detailed analysis of model of the hydrodynamical vortice on a plane is
executed. The derivation of the corresponding equation and its simplified
variant is given, a partial solutions are constructed. The question on
application of Darboux transformation is considered.


title:
Direct integral method, complete discrimination system for polynomial
  and applications to classifications of all single traveling wave solutions to
  nonlinear differential equations:a survey

abstract:
  Complete discrimination system for polynomial and direct integral method were
discussed systematically. In particularly, we pointed out some mistaken
viewpoints. Combining with complete discrimination system for polynomial,
direct integral method was developed to become a powerful method and was
applied to a lot of nonlinear mathematical physics equations. All single
traveling wave solutions to theses equations can be obtained. As examples, we
gave all traveling wave solutions to some equations such as mKdV equation,
Sine-Gordon equation, Double Sine-Gordon equation, triple Sine-Gordon equation,
Fujimoto-Watanabe equation, coupled Harry-Dym equation and coupled KdV equation
and so on. At the end, we give the partial answers to Fan's a problem.


title: Matter-wave bright solitons of $^7$Li gas in an expulsive potential

abstract:
  A Lagrangian based method is used to derive an analytical model for studying
the dynamics of matter-wave bright soliton created in a harmonic potential
which is attractive in the transverse direction and expulsive in the
longitudinal direction. By means of sech trial functions and a Ritz
optimization procedure, evolution eqautions are constructed for width,
amplitude and nonlinear frequency chirp of the propagating soliton of the
atomic condensate. Our eqaution for the width is an exact agreement with that
of Carr and Castin $[ Phys. Rev. A {\bf{66}}, 063602 (2002)]$, obtained by more
detailed analysis. In agreement with the experiment of Paris group $[ Science
{\bf{296}}, 1290 (2002)]$, the expulsive potential is found to cause the
soliton to explode for $N|a_s|=0.98$, $N$ being the number of atoms in the
condensate and $a_s$, the scattering length of the atom-atom interaction.


title: Remarks on the conserved densities of the Camassa-Holm equation

abstract:
  It is pointed out that the higher-order symmetries of the Camassa-Holm (CH)
equation are nonlocal and nonlocality poses problems to obtain higher-order
conserved densities for this integrable equation (J. Phys. A: Math. Gen. 2005,
{\bf 38} 869-880). This difficulty is circumvented by defining a nolinear
hierarchy for the CH equation and an explicit expression is constructed for the
nth-order conserved density.


title:
"Stokes' Second Problem in High Frequency Limit. Application to Micro
  (Nano)- Resonators

abstract:
  Using kinetic equation in the relaxation approximation (RTA), we investigate
a flow generated by an infinite plate oscillating with frequency $\omega$.
Geometrical simplicity of the problem allows a solution in the entire range of
dimensionless frequency variation $0\leq \omega \tau\leq \infty$, where $\tau$
is a properly defined relaxation time. A transition from viscoelastic behavior
of Newtonian fluid ($\omega\tau\to 0$) to purely elastic dynamics in the limit
$\omega\tau\to \infty$ is discovered.
  The relation of the derived solutions to microfluidics (high-frequency
micro-resonators) is demonstrated on an example of a "plane oscillator .

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


title:
Chaotic beats in a nonautonomous system governing second-harmonic
  generation of light

abstract:
  The letter proposes a procedure for generation and control chaotic beats in a
dynamical system being initially in the periodic state. The dynamical system
describes a simple nonlinear optical process -- second-harmonic generation of
light. The periodic states of the system have been found in analytical forms.
We also investigate some aspects of synchronization of chaotic beats in two
systems, detuned in the pump fields.


title: Reality problems in the soliton theory

abstract:
  This is a survey article dedicated mostly to the theory of real regular
"finite-gap" (algebro-geometrical) periodic and quasiperiodic Sine-Gordon
solutions. Long period this theory remained unfinished and ineffective, and by
that reason practically had no applications. Even for such simple physical
quantity as "Topological Charge" no formulas existed expressing it through the
"Inverse Spectral Data". Few years ago the present authors solved this problem
and made this theory effective. This article contains description of the
history and recent achievements. It describes also the reality problems for
several other fundamental soliton systems.


title: Examples of Synchronization in Discrete Chaotic Systems

abstract:
  This paper presents an application of partial contraction analysis to the
study of global synchronization in discrete chaotic systems. Explicit
sufficient conditions on the coupling strength of networks of discrete
oscillators are derived. Numerical examples and applications to simple systems
are presented. Previous researches have shown numerically that the systems
under study, when arranged in a network, exhibits rich and complex patterns
that can dynamically change in response to variations in the environment. We
show how this ``adaptation'' process strongly depends on the coupling
characteristics of the network. Other potential applications of synchronized
chaotic oscillators are discussed.


title: Classification of integrable super-systems using the SsTools environment

abstract:
  A classification problem is proposed for supersymmetric evolutionary PDE that
satisfy the assumptions of nonlinearity and nondegeneracy. Four classes of
nonlinear coupled boson-fermion systems are discovered under the homogeneity
assumption |f|=|b|=|D_t|=1/2. The syntax of the Reduce package SsTools, which
was used for intermediate computations, and the applicability of its procedures
to the calculus of super-PDE are described.


title:
Manifestations of Drag Reduction by Polymer Additives in Decaying,
  Homogeneous, Isotropic Turbulence

abstract:
  The existence of drag reduction by polymer additives, well established for
wall-bounded turbulent flows, is controversial in homogeneous, isotropic
turbulence. To settle this controversy we carry out a high-resolution direct
numerical simulation (DNS) of decaying, homogeneous, isotropic turbulence with
polymer additives. Our study reveals clear manifestations of
drag-reduction-type phenomena: On the addition of polymers to the turbulent
fluid we obtain a reduction in the energy dissipation rate, a significant
modification of the fluid energy spectrum especially in the deep-dissipation
range, a suppression of small-scale intermittency, and a decrease in
small-scale vorticity filaments.


title:
Numerical Investigation of Scaling Regimes in a Model of Anisotropically
  Advected Vector Field

abstract:
  Influence of strong uniaxial small-scale anisotropy on the stability of
inertial-range scaling regimes in a model of a passive transverse vector field
advected by an incompressible turbulent flow is investigated by means of the
field theoretic renormalization group. Turbulent fluctuations of the velocity
field are taken in the form of a Gaussian statistics with zero mean and defined
noise with finite correlations in time. It is shown that stability of the
inertial-range scaling regimes in the three-dimensional case is not destroyed
by anisotropy but the corresponding stability of the two-dimensional system can
be corrupted by the presence of anisotropy. A borderline dimension $d_c$ below
which the stability of the scaling regime is not present is calculated as a
function of anisotropy parameters.


title: Cellular Automata Modeling of Continuous Stirred Tank Reactors

abstract:
  The classical dynamical systems model of continuous stirred tank reactors
(CSTR) in which a first order chemical reaction takes place is reformulated in
terms of stochastic cellular automata by extending previous works of Seyborg
(1997) and Neuforth (2000) by including the feed flow of chemical reactants. We
show that this cellular automata procedure is able to simulate the dilution
rate and the mixing process in the CSTR, as well as the details of the heat
removal due to the jacket. The cellular automata approach is expected to be of
considerable applicability at any industrial scales and especially for any type
of microchemical systems


title: Inverse turbulent cascades and conformally invariant curves

abstract:
  We offer a new example of conformal invariance far from equilibrium -- the
inverse cascade of Surface Quasi-Geostrophic (SQG) turbulence. We show that
temperature isolines are statistically equivalent to curves that can be mapped
into a one-dimensional Brownian walk (called Schramm-Loewner Evolution or
SLE$_\kappa$). The diffusivity is close to $\kappa=4$, that is iso-temperature
curves belong to the same universality class as domain walls in the O(2) spin
model. Several statistics of temperature clusters and isolines are measured and
shown to be consistent with the theoretical expectations for such a spin system
at criticality. We also show that the direct cascade in two-dimensional
Navier-Stokes turbulence is not conformal invariant. The emerging picture is
that conformal invariance may be expected for inverse turbulent cascades of
strongly interacting systems.


title:
Moving and colliding pulses in the subcritical Ginzburg-Landau model
  with a standing-wave drive

abstract:
  We show the existence of steadily moving solitary pulses (SPs) in the complex
Ginzburg-Landau (CGL) equation, which includes the cubic-quintic (CQ)
nonlinearity and a conservative linear driving term, whose amplitude is a
standing wave with wavenumber $k$ and frequency $\omega $, the motion of the
SPs being possible at velocities $\pm \omega /k$, which provide locking to the
drive. A realization of the model may be provided by traveling-wave convection
in a narrow channel with a standing wave excited in its bottom (or on the
surface). An analytical approximation is developed, based on an effective
equation of motion for the SP coordinate. Direct simulations demonstrate that
the effective equation accurately predicts characteristics of the driven motion
of pulses, such as a threshold value of the drive's amplitude. Collisions
between two solitons traveling in opposite directions are studied by means of
direct simulations, which reveal that they restore their original shapes and
velocity after the collision.


title:
The Lorentz - invariant deformation of the Whitham system for the
  non-linear Klein-Gordon equation

abstract:
  We consider the deformation of the Whitham system for the non-linear
Klein-Gordon equation having the Lorentz-invariant form. Using the Lagrangian
formalism of the initial system we obtain the first non-trivial correction to
the Whitham system in the Lorentz-invariant approach.


title: Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations

abstract:
  Generalized synchronization is analyzed in unidirectionally coupled
oscillatory systems exhibiting spatiotemporal chaotic behavior described by
Ginzburg-Landau equations. Several types of coupling betweenthe systems are
analyzed. The largest spatial Lyapunov exponent is proposed as a new
characteristic of the state of a distributed system, and its calculation is
described for a distributed oscillatory system. Partial generalized
synchronization is introduced as a new type of chaotic synchronization in
spatially nonuniform distributed systems. The physical mechanisms responsible
for the onset of generalized chaotic synchronization in spatially distributed
oscillatory systems are elucidated. It is shown that the onset of generalized
chaotic synchronization is described by a modified Ginzburg-Landau equation
with additional dissipation irrespective of the type of coupling. The effect of
noise on the onset of a generalized synchronization regime in coupled
distributed systems is analyzed.


title: Control of chaotic advection

abstract:
  A method of chaos reduction for Hamiltonian systems is applied to control
chaotic advection. By adding a small and simple term to the stream function of
the system, the construction of invariant tori has a stabilization effect in
the sense that these tori act as barriers to diffusion in phase space and the
controlled Hamiltonian system exhibits a more regular behaviour.


title: Quantisation of bending flows

abstract:
  We briefly review the Kapovich-Millson notion of Bending flows as an
integrable system on the space of polygons in ${\bf R}^3$, its connection with
a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$.
Then we consider the quantisation problem of the set of Hamiltonians pertaining
to the problem, quite naturally called Bending Hamiltonians, and prove that
their commutativity is preserved at the quantum level.


title:
Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I)
  Trace formula

abstract:
  We consider a nonlinear area preserving Anosov map M on the torus phase
space, which is the simplest example of a fully chaotic dynamics. We are
interested in the quantum dynamics for long time, generated by the unitary
quantum propagator Mq. The usual semi-classical Trace formula expresses
Tr(Mq^t) for finite time t, in the limit hbar->0, in terms of periodic orbits
of M of period t. Recent work reach time t<< tE/6 where tE=log(1/hbar)/lambda
is the Ehrenfest time, and lambda is the Lyapounov coefficient. Using a
semi-classical normal form description of the dynamics uniformly over phase
space, we show how to extend the trace formula for longer time of the form t=
C.tE where C is any constant, with an arbitrary small error.


title: Segregation of two seed growth patterns with fractal geometry

abstract:
  We study the generalized diffusion-limited aggregates (DLA), with two seeds
placed at distance d lattice units and investigate the probability p(d) that
the patterns generated from those seeds get connected. In this model, one can
vary the parameter $\alpha$, and get a range of patterns from fractal-DLA to
compact one. For a fractal-DLA, p(d) decays rapidly with d, the decay is slower
for compact pattern in which case p(d)>>1 for all practical distances. We
demonstrate a similar phenomenon experimentally in viscous fingering and
electrochemical deposition with two injection points/cathodes.


title:
Tail resonances of FPU q-breathers and their impact on the pathway to
  equipartition

abstract:
  Upon initial excitation of a few normal modes the energy distribution among
all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits
exponential localization on large time scales. At the same time resonant
anomalies (peaks) are observed in its weakly excited tail for long times
preceding equipartition. We observe a similar resonant tail structure also for
exact time-periodic Lyapunov orbits, coined q-breathers due to their
exponential localization in modal space. We give a simple explanation for this
structure in terms of superharmonic resonances. The resonance analysis agrees
very well with numerical results and has predictive power. We extend a
previously developed perturbation method, based essentially on a
Poincare-Lindstedt scheme, in order to account for these resonances, and in
order to treat more general model cases, including truncated Toda potentials.
Our results give qualitative and semiquantitative account for the superharmonic
resonances of q-breathers and natural packets.


title:
Noise-induced cooperative dynamics and its control in coupled neuron
  models

abstract:
  We investigate feedback control of the cooperative dynamics of two coupled
neural oscillators that is induced merely by external noise. The interacting
neurons are modelled as FitzHugh-Nagumo systems with parameter values at which
no autonomous oscillations occur, and each unit is forced by its own source of
random fluctuations. Application of delayed feedback to only one of two
subsystems is shown to be able to change coherence and timescales of noise
induced oscillations either in the given subsystem, or globally. It is also
able to induce or to suppress stochastic synchronization under certain
conditions.


title:
Interaction-induced localization of anomalously-diffracting nonlinear
  waves

abstract:
  We study experimentally the interactions between normal solitons and tilted
beams in glass waveguide arrays. We find that as a tilted beam, traversing away
from a normally propagating soliton, coincides with the self-defocusing regime
of the array, it can be refocused and routed back into any of the intermediate
sites due to the interaction, as a function of the initial phase difference.
Numerically, distinct parameter regimes exhibiting this behavior of the
interaction are identified.


title: Coalescing Cellular Automata

abstract:
  We say that a Cellular Automata (CA) is coalescing when its execution on two
distinct (random) initial configurations in the same asynchronous mode (the
same cells are updated in each configuration at each time step) makes both
configurations become identical after a reasonable time. We prove coalescence
for two elementary rules and show that there exists infinitely many coalescing
CA. We then conduct an experimental study on all elementary CA and show that
some rules exhibit a phase transition, which belongs to the universality class
of directed percolation.


title: On the relation between the complex Toda and Volterra lattices

abstract:
  We give an analytic, sufficient condition for the existence of the Backlund
transformation between the semiinfinite Toda and Volterra lattices, in the
complex case, extending previous results given for the real case.


title: Painleve Analysis and Similarity Reductions for the Magma Equation

abstract:
  In this paper, we examine a generalized magma equation for rational values of
two parameters, $m$ and $n$. Firstly, the similarity reductions are found using
the Lie group method of infinitesimal transformations. The Painlev\'e ODE test
is then applied to the travelling wave reduction, and the pairs of $m$ and $n$
which pass the test are identified. These particular pairs are further
subjected to the ODE test on their other symmetry reductions. Only two cases
remain which pass the ODE test for all such symmetry reductions and these are
completely integrable. The case when $m=0$, $n=-1$ is related to the
Hirota-Satsuma equation and for $m=\tfrac12$, $n=-\tfrac12$, it is a real,
generalized, pumped Maxwell-Bloch equation.


title:
Complex variables for separation of Hamilton-Jacobi equation on real
  pseudo-Riemannian manifolds

abstract:
  In this paper the geometric theory of separation of variables for
time-independent Hamilton-Jacobi equation is extended to include the case of
complex eigenvalues of a Killing tensor on pseudo-Riemannian manifolds. This
task is performed without to complexify the manifold but just considering
complex-valued functions on it. The simple formalism introduced allows to
extend in a very natural way the classical results on separation of variables
(including Levi-Civita criterion and Stackel-Eisenhart theory) to the complex
case. Orthogonal variables only are considered.


title:
Peeping at chaos: Nondestructive monitoring of chaotic systems by
  measuring long-time escape rates

abstract:
  One or more small holes provide non-destructive windows to observe
corresponding closed systems, for example by measuring long time escape rates
of particles as a function of hole sizes and positions. To leading order the
escape rate of chaotic systems is proportional to the hole size and independent
of position. Here we give exact formulas for the subsequent terms, as sums of
correlation functions; these depend on hole size and position, hence yield
information on the closed system dynamics. Conversely, the theory can be
readily applied to experimental design, for example to control escape rates.


title: Synchronization in semiconductor laser rings

abstract:
  We examine the dynamics of semiconductor lasers coupled in a ring
configuration. The lasers, which have stable output intensity when isolated,
behave chaotically when coupled unidirectionally in a closed chain. In this
way, we show that neither feedback nor bidirectional coupling is necessary to
induce chaotic dynamics at the laser output. We study the synchronization
phenomena arising in this particular coupling architecture, and discuss its
possible application to chaos-based communications. Next, we extend the study
to bidirectional coupling and propose an appropriate technique to optical chaos
encryption/decryption in closed chains of mutually coupled semiconductor
lasers.


title: Gravity surface wave turbulence in a laboratory flume

abstract:
  We present experimental results for water wave turbulence excited by
piston-like programmed wavemakers in a water flume with horisontal dimensions
6x12x1.5 meters. Our main finding is that for a wide range of excitation
amplitudes the energy spectrum has a power-law scaling, $E_\omega \sim
\omega^{-\nu}$. These scalings were achieved in up to one-decade wide frequency
range, which is significantly wider than the range available in field
observations and in numerical simulations. However, exponent $\nu$ appears to
be non-universal. It depends on the wavefield intensity and ranges from about
6.5 for weak forcing to about 3.5 for large levels of wave excitations. We
discuss our results in the context of the key theoretical predictions, such as
Zakharov-Filonenko spectrum $\nu=-4$, Phillips spectrum $\nu = -5$, Kuznetsov's
revision of Phillips spectrum (leading to $\nu=-4$) and Nazarenko's prediction
$\nu=-6$ for weak turbulence in finite basins. We measured Probability Density
Function of the surface elevation and good correspondence with the Tayfun
shapeexcept values near the maximum which we attribute to an anisotropy and
inhomogeneity caused by the finite flume size. We argue that the wavenumber
discreteness, due to the finite-size of the flume, prevents four-wave resonant
interactions. Therefore, statistical evolution of the water surface in the
laboratory is significantly different than in the open ocean conditions.


title:
Freely decaying turbulence and Bose-Einstein condensation in
  Gross-Pitaevski model

abstract:
  We study turbulence and Bose-Einstein condensation (BEC) within the
two-dimensional Gross-Pitaevski (GP) model. In the present work, we compute
decaying GP turbulence in order to establish whether BEC can occur without
forcing and if there is an intensity threshold for this process. We use the
wavenumber-frequency plots which allow us to clearly separate the condensate
and the wave components and,therefore, to conclude if BEC is present. We
observe that BEC in such a system happens even for very weakly nonlinear
initial conditions without any visible threshold.
  BEC arises via a growing phase coherence due to anihilation of phase
defects/vortices. We study this process by tracking of propagating vortex
pairs. The pairs loose momentum by scattering the background sound, which
results in gradual decrease of the distance between the vortices. Occasionally,
vortex pairs collide with a third vortex thereby emitting sound, which can lead
to more sudden shrinking of the pairs. After the vortex anihilation the pulse
propagates further as a dark soliton, and it eventually bursts creating a
shock.


title:
The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2)
  Symmetry

abstract:
  We investigate the integrable structure of spin chain models with centrally
extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the
planar AdS/CFT correspondence, but they also contain the one-dimensional
Hubbard model as a special case. We begin with an overview of the
representation theory of centrally extended su(2|2). These results are applied
in the construction and investigation of an interesting S-matrix with su(2|2)
symmetry. In particular, they enable a remarkably simple proof of the
Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry's
R-matrix and thus uncover a hidden supersymmetry in the integrable structure of
the Hubbard model. We then construct eigenvalues of the corresponding transfer
matrix in order to formulate an analytic Bethe ansatz. Finally, the form of
transfer matrix eigenvalues for models with psu(2,2|4) symmetry is sketched.


title:
Homoclinic transition to chaos in the Ueda oscillator with external
  forcing

abstract:
  We examine the Melnikov criterion for transition to chaos in case of a single
degree of freedom nonlinear oscillator with the Ueda well potential and an
external periodic excitation term. Using effective Hamiltonian we have examined
homoclinic orbits and cross-sections of stable and unstable manifolds which
gave the condition of transition to chaos through a homoclinic bifurcation.


title: Stochastic description of the deterministic Ricker's population model

abstract:
  We adopt the '0-1' test for chaos using Brownian motion chains to identify
the dynamics of the Ricker's population model. In the '0-1' test '0' is related
to regular motion while '1' is associated with chaotic motion. The identified
regular and chaotic types of solutions have been confirmed by means of
recurrence plots.


title:
Suppression of Complex Spiral--Wave Activity in an Ionic Model of
  Cardiac Tissue by Weak Local Stimulations

abstract:
  On the basis of a quite realistic ionic Fenton--Karma model of the cardiac
tissue we consider the problem of defibrillation by a local weak forcing. In
contrast to other systems, this model accurately reproduces the most essential
mesoscopic properties of the cardiac activity. It is shown that suppression of
spiral--wave turbulent dynamics in the heart tissue may be realized by a
low-voltage local non-feedback electrical stimulation of monophasic and
biphasic shapes. After stabilization the medium goes to a spatially homogeneous
steady state.


title:
Equations Of Long Waves With A Free Surface IV. The Case of Constant
  Shear

abstract:
  A large class of two-dimensional free-surface hydrodynamical systems is
determined that can be self-consistently reduced by the condition that the
velocity profile has a constant shear. The reduced systems turn out to be
Hamiltonian, and so does the reduction process itself. All reducible systems,
Hamiltonian or not, are determined and %%@ shown to form a Lie algebra. All
this is then generalized to the multilayer/multi-species representations.


title: The Structure, the Dynamics and the Survivability of Social Systems

abstract:
  Social systems must fulfil four basic functions to ensure their survival in
competitive conditions. Social systems must provide for: (1) energy and other
necessities of life, (2) security against external and internal threats, (3)
identity and self-development, and (4) consistency and direction. These
functions result in four more or less autonomous aspect systems; these aspect
systems interact. Between the variables of basic functions and variables of
aspect systems, a minimal level of consistency is required to facilitate growth
and development, and to ensure the (future) survivability of the social system.
Sooner or later, growth, change, and differentiated development result in
inconsistencies within/between basic functions and aspect systems. These
inconsistencies affect the effectiveness and efficiency of these social systems
to provide for the basic functions. Periodically, deliberate or spontaneous
corrective adjustments of social systems are required, to correct for these
inconsistencies.


title: Dynamo effect in the Kraichnan magnetohydrodynamic turbulence

abstract:
  The existence of a dynamo effect in a simplified magnetohydrodynamic model of
turbulence is considered when the magnetic Prandtl number approaches zero or
infinity. The magnetic field is interacting with an incompressible
Kraichnan-Kasantzev model velocity field augmented with a viscous scale cutoff.
An approximate system of equations in the different scaling ranges can be
formulated and solved, so that the solution tends to the exact one when the
viscous and magnetic-diffusive cutoffs approach zero. In this approximation we
are able to determine analytically the conditions for the existence of a dynamo
effect and give an estimate of the dynamo growth rate. Among other things we
show that in the large Prandtl number case the dynamo effect is always present.
Our analytical estimates are in good agreement with previous numerical studies
of the Kraichnan-Kasantzev dynamo by D. Vincenzi.


title:
Isochronal synchrony and bidirectional communication with delay-coupled
  nonlinear oscillators

abstract:
  We propose a basic mechanism for isochronal synchrony and communication with
mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators
(IROs), mutually coupled with a propagation delay, synchronize isochronally
when both are symmetrically driven by a third Ikeda oscillator. This
synchronous operation, unstable in the two delay-coupled oscillators alone,
facilitates simultaneous, bidirectional communication of messages with chaotic
carrier waveforms. This approach to combine both bidirectional and
unidirectional coupling represents an application of generalized
synchronization using a mediating drive signal for a spatially distributed and
internally synchronized multi-component system.


title:
Study on Applications of Supply and Demand Theory of Microeconomics and
  Physics Field Theory to Central Place Theory

abstract:
  This paper attempts to analyze central place theory of spatial economics
based on supply and demand theory in microeconomics and field theory in
physics, and also discuss their relationship. Three most important research
findings are described below. Firstly, the concept of market equilibrium could
be expressed in the mathematical form of physics field theory under proper
hypothesis. That is because the most important aspect of field theory model is
that complex analysis is taken as a key mathematical tool. If assuming that
imaginary part is neglected in this model, it is found that this model has the
same mathematical structure as supply and demand theory of microeconomics.
Secondly, the mathematical model of field theory can be applied to express
clearly many concepts of central place theory, or even introduce many new
concepts. Thirdly, it could also be taken as a study of combining the Hotelling
Model and Moses Model for the location theory in another mathematic approach.


title: Synchronization in the presence of memory

abstract:
  We study the effect of memory on synchronization of identical chaotic systems
driven by common external noises. Our examples show that while in general
synchronization transition becomes more difficult to meet when memory range
increases, for intermediate ranges the synchronization tendency of systems can
be enhanced. Generally the synchronization transition is found to depend on the
memory range and the ratio of noise strength to memory amplitude, which
indicates on a possibility of optimizing synchronization by memory. We also
point out on a close link between dynamics with memory and noise, and recently
discovered synchronizing properties of networks with delayed interactions.


title:
Transversal interface dynamics of a front connecting a stripe pattern to
  a uniform state

abstract:
  Interfaces in two-dimensional systems exhibit unexpected complex dynamical
behaviors, the dynamics of a border connecting a stripe pattern and a uniform
state is studied. Numerical simulations of a prototype isotropic model, the
subcritical Swift-Hohenberg equation, show that this interface has transversal
spatial periodic structures, zigzag dynamics and complex coarsening process.
Close to a spatial bifurcation, an amended amplitude equation and a
one-dimensional interface model allow us to characterize the dynamics exhibited
by this interface.


title:
The classification of all single travelling wave solutions to
  Calogero-Degasperis-Focas equation

abstract:
  Under the travelling wave transformation, Calogero-Degasperis-Focas equation
was reduced to an ordinary differential equation. Using a symmetry group of
one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE.
Furthermore, we applied the change of the variable and complete discrimination
system for polynomial to solve the corresponding integrals and obtained the
classification of all single travelling wave solutions to
Calogero-Degasperis-Focas equation.


title:
The Generalized Dirichlet to Neumann map for the KdV equation on the
  half-line

abstract:
  For the two versions of the KdV equation on the positive half-line an
initial-boundary value problem is well posed if one prescribes an initial
condition plus either one boundary condition if $q_{t}$ and $q_{xxx}$ have the
same sign (KdVI) or two boundary conditions if $q_{t}$ and $q_{xxx}$ have
opposite sign (KdVII). Constructing the generalized Dirichlet to Neumann map
for the above problems means characterizing the unknown boundary values in
terms of the given initial and boundary conditions. For example, if
$\{q(x,0),q(0,t) \}$ and $\{q(x,0),q(0,t),q_{x}(0,t) \}$ are given for the KdVI
and KdVII equations, respectively, then one must construct the unknown boundary
values $\{q_{x}(0,t),q_{xx}(0,t) \}$ and $\{q_{xx}(0,t) \}$, respectively. We
show that this can be achieved without solving for $q(x,t)$ by analysing a
certain ``global relation'' which couples the given initial and boundary
conditions with the unknown boundary values, as well as with the function
$\Phi^{(t)}(t,k)$, where $\Phi^{(t)}$ satisifies the $t$-part of the associated
Lax pair evaluated at $x=0$. Indeed, by employing a Gelfand--Levitan--Marchenko
triangular representation for $\Phi^{(t)}$, the global relation can be solved
\emph{explicitly} for the unknown boundary values in terms of the given initial
and boundary conditions and the function $\Phi^{(t)}$. This yields the unknown
boundary values in terms of a nonlinear Volterra integral equation.


title:
Statistical Approach of Modulational Instability in the Class of
  Derivative Nonlinear Schroedinger Equations

abstract:
  The modulational instability in the class of NLS equations is discussed using
a statistical approach. A kinetic equation for the two-point correlation
function is studied in a linear approximation, and an integral stability
equation is found. The modulational instability is associated with a positive
imaginary part of the frequency. The integral equation is solved for different
types of initial distributions (delta-function, Lorentzian) and the results are
compared with those obtained using a deterministic approach. The differences
between modulation instability of the normal NLS equation and derivative NLS
equations is emphasized.


title: Integrable Models of Interaction of Matter with Radiation

abstract:
  The simplified models of interaction of charged matter with resonance modes
of radiation generalizing the well-known Jaynes-Cummings and Dicke models are
considered. It is found that these new models are integrable for arbitrary
numbers of dipole sources and resonance modes of the radiation field. The
problem of explicit diagonalisation of corresponding Hamiltonians is discussed.


title:
Domain Wall and Periodic Solutions of Coupled Asymmetric Double Well
  Models

abstract:
  Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional
potentials arise in the context of first order phase transitions both in
condensed matter physics and field theory. Here we provide an exhaustive set of
exact periodic solutions of such a coupled asymmetric model in terms of
elliptic functions (domain wall arrays) and obtain single domain wall solutions
in specific limits. We also calculate the energy and interaction between
solitons for various solutions. Both topological (kink-like at $T=T_c$) and
nontopological (pulse-like for $T\ne T_c$) domain wall solutions are obtained.
We relate some of these solutions to domain walls in hydrogen bonded materials
and also in the field theory context. As a byproduct, we also obtain a new one
parameter family of kink solutions of the uncoupled asymmetric double well
model.

categories: nlin.PS cond-mat.stat-mech hep-th nlin.SI


title:
Synchronization of mutually coupled chaotic lasers in the presence of a
  shutter

abstract:
  Two mutually coupled chaotic diode lasers exhibit stable isochronal
synchronization in the presence of self feedback. When the mutual communication
between the lasers is discontinued by a shutter and the two uncoupled lasers
are subject to self-feedback only, the desynchronization time is found to scale
as $A_d\tau$ where $A_d>1$ and $\tau$ corresponds to the optical distance
between the lasers. Prior to synchronization, when the two lasers are
uncorrelated and the shutter between them is opened, the synchronization time
is found to be much shorter, though still proportional to $\tau$. As a
consequence of these results, the synchronization is not significantly altered
if the shutter is opend/closed faster than the desynchronization time.
Experiments in which the coupling between two chaotic-synchronized diode lasers
is modulated with an electro-optic shutter are found to be consistent with the
results of numerical simulations.


title:
The Soliton Equations associated with the Affine Kac-Moody Lie Algebra
  G_2^{(1)}

abstract:
  We construct in an explict way the soliton equation corresponding to the
affine Kac--Moody Lie algebra $G_2^{(1)}$ together with their bihamiltonian
structure. Moreover the Riccati equation satisfied by the generating function
of the commuting Hamiltonians densities is also deduced. Finally we describe a
way to deduce the bihamiltonian equations directly in terms of this latter
functions


title:
Characterising the Difference between Complex Adaptive and Conventional
  Combat Models

abstract:
  An attempt is made to quantitatively demonstrate the difference between a
complex adaptive combat model and conventional combat models. The work shows
that complex adaptive models may give rise to "turbulent" dynamics, which
emerge once the battlefield is no longer "linear", i.e. once military
formations no longer form ordered lines or columns. This is done using a
cellular automaton model. This model exhibits a high degree of complexity,
leading to a rich variety of behaviour. Conventional statistical methods fail
to adequately capture this richness. Particular attention is paid to the
properties of the attrition function. It is found that this function is
discontinuous and possesses non-linear properties such as clustering of
casualties, scaling of the statistical moments of the data and fat-tailed
probability distributions. Fractal methods are found to be capable of
quantifying these properties. A particularly significant result is the
non-linearity of the pay-off of improved weapons performance. This contrasts
with conventional models, where the attrition rate usually depends in a linear
way on kill probability. Additionally, the model is found to possess at least
two attractive states. A transition exists between the two cases in some
situations. This transition appears to behave in an analogous way to the
transition between laminar and turbulent states in fluid dynamics.


title:
A Metamodel for Describing the Outcomes of the Mana Cellular Automaton
  Combat Model Based on Lauren's Attrition Equation

abstract:
  In 1999 the author suggested an equation to describe the rate and temporal
distribution of battle casualties. This equation was proposed as a replacement
for the Lanchester equation. Unlike Lanchester's equation, the author's
equation is based on a measurement of the spatial distribution of forces
involved in a battle, and incorporates this by use of the concept of the
fractal dimension. In this report, the form of the expected Loss-Exchange-Ratio
function based on this equation is determined. It is shown how this function
can be used as a Metamodel to describe the outcome of some cellular automaton
models. While this is not an exhaustive proof of the validity of the equation,
the match for the case studied is convincing, pointing to the potential of the
equation to be adopted more generally for combat models. This is particularly
so in the context of earlier work studying historical battle data that also
supports an equation of the form of the author's proposal.


title:
Local excitation-lateral inhibition interaction yields wave
  instabilities in spatial systems involving finite propagation delay

abstract:
  The work studies wave activity in spatial systems, which exhibit nonlocal
spatial interactions at the presence of a finite propagation speed. We find
analytically propagation delay-induced wave instabilities for various local
excitatory and lateral inhibitory spatial interactions. The final numerical
simulation confirms the analytical results.


title: 1/f noise and multifractality in atmospheric-CO2 records

abstract:
  We study the fluctuations in the measured atmospheric CO2 records from
several stations and show that it displays 1/f noise and multifractality. Using
detrended fluctuation analysis and wavelet based methods, we estimate
thescaling exponents at various time scales. We also simulate CO2 time series
from an atmospheric chemistry-transport model (CTM) and show that eventhough
the model results are in broad agreement with the measured exponents there are
still some discrepancies between them. The implications for sources and sinks
inversion of atmospheric-CO2 is discussed.

categories: nlin.AO cond-mat.stat-mech nlin.CD physics.ao-ph


title:
Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks
  in internal waves in deep fluid

abstract:
  The Whitham modulation equations for the parameters of a periodic solution
are derived using the generalized Lagrangian approach for the case of damped
Benjamin-Ono equation. The structure of the dispersive shock in internal wave
in deep water is considered by this method.


title: Self-organizing traffic lights: A realistic simulation

abstract:
  We have previously shown in an abstract simulation (Gershenson, 2005) that
self-organizing traffic lights can improve greatly traffic flow for any
density. In this paper, we extend these results to a realistic setting,
implementing self-organizing traffic lights in an advanced traffic simulator
using real data from a Brussels avenue. On average, for different traffic
densities, travel waiting times are reduced by 50% compared to the current
green wave method.

categories: nlin.AO cond-mat.stat-mech cs.AI physics.comp-ph physics.soc-ph


title: An ultradiscrete matrix version of the fourth Painleve equation

abstract:
  We establish a matrix generalization of the ultradiscrete fourth Painlev\'e
equation (ud-PIV). Well-defined multicomponent systems that permit
ultradiscretization are obtained using an approach that relies on a group
defined by constraints imposed by the requirement of a consistent evolution of
the systems. The ultradiscrete limit of these systems yields coupled
multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics,
irreducibility, and integrability of the matrix valued ultradiscrete systems
are studied.


title:
Effect of pitchfork bifurcations on the spectral statistics of
  Hamiltonian systems

abstract:
  We present a quantitative semiclassical treatment of the effects of
bifurcations on the spectral rigidity and the spectral form factor of a
Hamiltonian quantum system defined by two coupled quartic oscillators, which on
the classical level exhibits mixed phase space dynamics. We show that the
signature of a pitchfork bifurcation is two-fold: Beside the known effect of an
enhanced periodic orbit contribution due to its peculiar $\hbar$-dependence at
the bifurcation, we demonstrate that the orbit pair born {\em at} the
bifurcation gives rise to distinct deviations from universality slightly {\em
above} the bifurcation. This requires a semiclassical treatment beyond the
so-called diagonal approximation. Our semiclassical predictions for both the
coarse-grained density of states and the spectral rigidity, are in excellent
agreement with corresponding quantum-mechanical results.


title:
Theoretical analysis and multi-agent simulation of the ecosystem in
  Tibet

abstract:
  Bird Funeral is a strange funeral custom in Tibet of China. The lamaists hope
they can save small fauna such as pikas by sacrificing themselves to the
eagles. But can they save the fauna by their sacrifice? By theoretical analysis
and multi-agent simulation, we give a negative conclusion that the sacrifice
are, in fact, reducing the population of the pikas. In contemporary Tibet, the
eagle population is reducing drastically, and the pastures are degenerating.
People blame this on the excessive population of the plateau pikas. We propose
a model to explain this phenomenon. The eagles are dying off because of
overgrazing but not the pikas. We also point out that killing the pikas is
probably unhelpful to recover the pastures but worsen the degeneration of the
pastures. And if people want to recover the pastures, they have to increase
both the population of the predator and the supply of grass simultaneously.


title: Lotka-Volterra dynamics under periodic influence

abstract:
  Lotka Volterra model and its modified forms have long become a major area of
interest for periodic motions in nonlinear systems with competitive species.
The model given by Volterra shows that its periodicity is dependent on initial
condition. This characteristics allows us to calculate the effect of periodic
seasonal changes on population densities of different species


title: Burgers and KP hierarchies: A functional representation approach

abstract:
  From a 'discrete' functional zero curvature equation, functional
representations of (matrix) Burgers and potential KP (pKP) hierarchies (and
others), as well as corresponding Backlund transformations, can be obtained in
a surprisingly simple way. With their help we show that any solution of a
Burgers hierarchy is also a solution of the pKP hierarchy. Moreover, the pKP
hierarchy can be expressed in the form of an inhomogeneous Burgers hierarchy.
In particular, this leads to an extension of the Cole-Hopf transformation to
the pKP hierarchy. Furthermore, these hierarchies are solved by the solutions
of certain functional Riccati equations.


title:
On a new integrable nonlinear Schroedinger equation with a simple
  external potential and its explicit solutions

abstract:
  A nonlinear Schr\"odinger equation with external potential $-(t+b)^{-1}$ is
considered and its explicit solutions are constructed.


title:
A self-organized particle moving model on scale free network with
  $1/f^{2}$ behavior

abstract:
  In this paper we propose a self-organized particle moving model on scale free
network with the algorithm of the shortest path and preferential walk. The
over-capacity property of the vertices in this particle moving system on
complex network is studied from the holistic point of view. Simulation results
show that the number of over-capacity vertices forms punctuated equilibrium
processes as time elapsing, that the average number of over-capacity vertices
under each local punctuated equilibrium process has power law relationship with
the local punctuated equilibrium value. What's more, the number of
over-capacity vertices has the bell-shaped temporal correlation and $1/f^{2}$
behavior. Finally, the average lifetime $L(t)$ of particles accumulated before
time $t$ is analyzed to find the different roles of the shortest path algorithm
and the preferential walk algorithm in our model.


title: Hypergeometric solutions to ultradiscrete Painleve equations

abstract:
  We propose new solutions to ultradiscrete Painlev\'e equations that cannot be
derived using the ultradiscretization method. In particular, we show the third
ultradiscrete Painelev\'e equation possesses hypergeometric solutions. We show
this by considering a lift of these equations to a non-archimedean valuation
field in which we may relax the subtraction free framework of previous
explorations of the area. Using several methods, we derive a family of
hypergeometric solutions.


title:
Discrete surface solitons in two-dimensional anisotropic photonic
  lattices

abstract:
  We study nonlinear surface modes in two-dimensional {\em anisotropic}
periodic photonic lattices and demonstrate that, in a sharp contrast to
one-dimensional discrete surface solitons, the mode threshold power is lower at
the surface, and two-dimensional discrete solitons can be generated easier near
the lattice corners and edges. We analyze the crossover between effectively
one- and two-dimensional regimes of the surface-mediated beam localization in
the lattice.


title: SU(3) Richardson-Gaudin models: three level systems

abstract:
  We present the exact solution of the Richardson-Gaudin models associated with
the SU(3) Lie algebra. The derivation is based on a Gaudin algebra valid for
any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For
the rational case additional cubic integrals of motion are obtained, whose
number is added to that of the quadratic ones to match, as required from the
integrability condition, the number of quantum degrees of freedom of the model.
We discuss different SU(3) physical representations and elucidate the meaning
of the parameters entering in the formalism. By considering a bosonic mapping
limit of one of the SU(3) copies, we derive new integrable models for three
level systems interacting with two bosons. These models include a generalized
Tavis-Cummings model for three level atoms interacting with two modes of the
quantized electric field.


title:
Transitions between symmetric and asymmetric solitons in dual-core
  systems with cubic-quintic nonlinearity

abstract:
  It is well known that a symmetric soliton in coupled nonlinear Schroedinger
(NLS) equations with the cubic nonlinearity loses its stability with the
increase of its energy, featuring a transition into an asymmetric soliton via a
subcritical bifurcation. A similar phenomenon was found in a dual-core system
with quadratic nonlinearity, and in linearly coupled fiber Bragg gratings, with
a difference that the symmetry-breaking bifurcation is supercritical in those
cases. We aim to study transitions between symmetric and asymmetric solitons in
dual-core systems with saturable nonlinearity. We demonstrate that a basic
model of this type, viz., a pair of linearly coupled NLS equations with the
intra-core cubic-quintic (CQ) nonlinearity, features a bifurcation loop: a
symmetric soliton loses its stability via a supercritical bifurcation, which is
followed, at a larger value of the energy, by a reverse bifurcation that
restores the stability of the symmetric soliton. If the linear-coupling
constant is small enough, the second bifurcation is subcritical, and there is a
broad interval of energies in which the system is bistable, with coexisting
stable symmetric and asymmetric solitons. At larger values of the coupling
constant, the reverse bifurcation is supercritical, and the bifurcation loop
disappears if the linear coupling is very strong. Collisions between moving
solitons are studied too. Symmetric solitons always collide elastically, while
collisions between asymmetric solitons turns them into breathers, that
subsequently undergo dynamical symmetrization.


title: Vibration of Generalized Double Well Oscillators

abstract:
  We have applied the Melnikov criterion to examine a global homoclinic
bifurcation and transition to chaos in a case of a double well dynamical system
with a nonlinear fractional damping term and external excitation. The usual
double well Duffing potential having a negative square term and positive
quartic term has been generalized to a double well potential with a negative
square term and a positive one with an arbitrary real exponent $q > 2$. We have
also used a fractional damping term with an arbitrary power $p$ applied to
velocity which enables one to cover a wide range of realistic damping factors:
from dry friction $p \to 0$ to turbulent resistance phenomena $p=2$.
  Using perturbation methods we have found a critical forcing amplitude $\mu_c$
above which the system may behave chaotically. Our results show that the
vibrating system is less stable in transition to chaos for smaller $p$
satisfying an exponential scaling low. The critical amplitude $\mu_c$ as an
exponential function of $p$.
  The analytical results have been illustrated by numerical simulations using
standard nonlinear tools such as
  Poincare maps and the maximal Lyapunov exponent. As usual for chosen system
parameters we have identified a chaotic motion above the critical Melnikov
amplitude $\mu_c$.


title: Periodic-Orbit Theory of Level Correlations

abstract:
  We present a semiclassical explanation of the so-called
Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral
fluctuations in chaotic dynamics. We work with a generating function whose
semiclassical limit is determined by quadruplets of sets of periodic orbits.
The asymptotic expansions of both the non-oscillatory and the oscillatory part
of the universal spectral correlator are obtained. Borel summation of the
series reproduces the exact correlator of random-matrix theory.


title: $osp(1|2)$ off-shell Bethe ansatz equation with boundary terms

abstract:
  This work is concerned with the quasi-classical limit of the boundary quantum
inverse scattering method for the $osp(1|2)$ vertex model with diagonal
$K$-matrices. In this limit Gaudin's Hamiltonians with boundary terms are
presented and diagonalized. Moreover, integral representations for correlation
functions are realized to be solutions of the trigonometric
Knizhnik-Zamoldchikov equations.


title:
Response of a Magneto-Rheological Fluid Damper Subjected to Periodic
  Forcing in a High Frequency Limit

abstract:
  We explored vibrations of a single-degree of freedom oscillator with a
magneto-rheological damper subjected to kinematic excitations. Using fast and
slow scales decoupling procedure we derived an effective damping coefficient in
the limit of high frequency excitation. Damping characteristics, as functions
of velocity, change considerably especially by terminating the singular
non-smoothness points. This effect was more transparent for a larger control
parameter which was defined as the product of the excitation amplitude and its
frequency.


title:
Energy Conservation and Second-Order Statistics in Stably Stratified
  Turbulent Boundary Layers

abstract:
  We address the dynamical and statistical description of stably stratified
turbulent boundary layers with the important example of the atmospheric
boundary layer with a stable temperature stratification in mind. Traditional
approaches to this problem, based on the profiles of mean quantities, velocity
second-order correlations, and dimensional estimates of the turbulent thermal
flux run into a well known difficulty, predicting the suppression of turbulence
at a small critical value of the Richardson number, in contradiction with
observations. Phenomenological attempts to overcome this problem suffer from
various theoretical inconsistencies. Here we present an approach taking into
full account all the second-order statistics, which allows us to respect the
conservation of total mechanical energy. The analysis culminates in an analytic
solution of the profiles of all mean quantities and all second-order
correlations removing the unphysical predictions of previous theories. We
propose that the approach taken here is sufficient to describe the lower parts
of the atmospheric boundary layer, as long as the Richardson number does not
exceed an order of unity. For much higher Richardson numbers the physics may
change qualitatively, requiring careful consideration of the potential
Kelvin-Helmoholtz waves and their interaction with the vortical turbulence.


title: Synchronization processes in complex networks

abstract:
  We present an extended analysis, based on the dynamics towards
synchronization of a system of coupled oscillators, of the hierarchy of
communities in complex networks. In the synchronization process, different
structures corresponding to well defined communities of nodes appear in a
hierarchical way. The analysis also provides a useful connection between
synchronization dynamics, complex networks topology and spectral graph
analysis.


title:
Relations for zeros of special polynomials associated to the Painleve
  equations

abstract:
  A method for finding relations for the roots of polynomials is presented. Our
approach allows us to get a number of relations for the zeros of the classical
polynomials and for the roots of special polynomials associated with rational
solutions of the Painleve equations. We apply the method to obtain the
relations for the zeros of several polynomials. They are: the Laguerre
polynomials, the Yablonskii - Vorob'ev polynomials, the Umemura polynomials,
the Ohyama polynomials, the generalized Okamoto polynomials, and the
generalized Hermite polynomials. All the relations found can be considered as
analogues of generalized Stieltjes relations.


title: Moving solitons in the discrete nonlinear Schr\"odinger equation

abstract:
  Using the method of asymptotics beyond all orders, we evaluate the amplitude
of radiation from a moving small-amplitude soliton in the discrete nonlinear
Schr\"odinger equation. When the nonlinearity is of the cubic type, this
amplitude is shown to be nonzero for all velocities and therefore
small-amplitude solitons moving without emitting radiation do not exist. In the
case of a saturable nonlinearity, on the other hand, the radiation is found to
be completely suppressed when the soliton moves at one of certain isolated
`sliding velocities'. We show that a discrete soliton moving at a general speed
will experience radiative deceleration until it either stops and remains pinned
to the lattice, or--in the saturable case--locks, metastably, onto one of the
sliding velocities. When the soliton's amplitude is small, however, this
deceleration is extremely slow; hence, despite losing energy to radiation, the
discrete soliton may spend an exponentially long time travelling with virtually
unchanged amplitude and speed.


title: Single particle Lagrangian dispersion in Bolgiano turbulence

abstract:
  Single-particle dispersion in the Bolgiano--Obukhov regime of two-dimensional
turbulent convection is investigated. Unlike dispersion in a flow displaying
the classical K41 phenomenology, here, the leading contribution to the
Lagrangian velocity fluctuations is given by the largest eddies. This implies a
linear behavior in time for a typical velocity fluctuation in the time interval
$t$. The contribution to the Lagrangian velocity fluctuations of local eddies
(i.e. with a characteristic time of order $t$), whose space/time scalings are
ruled by the Bolgiano--Obukhov theory, is thus not detectable by standard
Lagrangian statistical observables. To disentangle contributions arising from
the large eddies from those of local eddies, a strategy based on exit-time
statistics has successfully been exploited. Lagrangian velocity increments in
Bolgiano convection thus provide a physically relevant example of signal with
\emph{more than smooth} fluctuations.


title:
Multicomponent integrable wave equations I. Darboux-Dressing
  Transformation

abstract:
  The Darboux-Dressing Transformations are applied to the Lax pair associated
to systems of coupled nonlinear wave equations in the case of boundary values
which are appropriate to both bright and dark soliton solutions. The general
formalism is set up and the relevant equations are explicitly solved. Several
instances of multicomponent wave equations of applicative interest, such as
vector nonlinear Schroedinger-type equations and three resonant wave equations
are considered.


title: Controlled Parameter Modulations in Secure Digital Signal Transmissions

abstract:
  We propose a simple method for secure digital signal transmission by making
some modifications in the single-step parameter modulation technique proposed
earlier into overcome certain inherent deficiencies. In the modified method,
the parameter modulation is effectively regulated or controlled by the chaotic
signal obtained from the transmitting chaotic system so that it has the maximum
security. Then, the same idea is also extended to the multistep parameter
modulation technique. It is found that both the methods are secure against
ciphertext (return map) and plaintex attacks. We have illustrated these methods
by means of the Lorenz system.


title: Quasipatterns in parametrically forced systems

abstract:
  We examine two mechanisms that have been put forward to explain the selection
of quasipatterns in single and multi-frequency forced Faraday wave experiments.
Both mechanisms can be used to generate stable quasipatterns in a
parametrically forced partial differential equation that shares some
characteristics of the Faraday wave experiment. One mechanism, which is robust
and works with single-frequency forcing, does not select a specific
quasipattern: we find, for two different forcing strengths, a 12-fold
quasipattern and the first known example of a spontaneously formed 14-fold
quasipattern. The second mechanism, which requires more delicate tuning, can be
used to select particular angles between wavevectors in the quasipattern.


title: Front explosion in a periodically forced surface reaction

abstract:
  Resonantly-forced oscillatory reaction-diffusion systems can exhibit fronts
with complicated interfacial structure separating phase-locked homogeneous
states. For values of the forcing amplitude below a critical value the front
"explodes" and the width of the interfacial zone grows without bound. Such
front explosion phenomena are investigated for a realistic model of catalytic
CO oxidation on a Pt(110) surface in the 2:1 and 3:1 resonantly-forced regimes.
In the 2:1 regime, the fronts are stationary and the front explosion leads to a
defect-mediated turbulent state. In the 3:1 resonantly-forced system, the
fronts propagate. The front velocity tends to zero as the front explosion point
is reached and the final asymptotic state is a 2:1 resonantly-locked
labyrinthine pattern. The front dynamics described here should be observable in
experiment since the model has been shown to capture essential features of the
CO oxidation reaction.


title: Quasi-exact solvability in a general polynomial setting

abstract:
  Our goal in this paper is to extend the theory of quasi-exactly solvable
Schrodinger operators beyond the Lie-algebraic class. Let $\cP_n$ be the space
of n-th degree polynomials in one variable. We first analyze "exceptional
polynomial subspaces" which are those proper subspaces of $\cP_n$ invariant
under second order differential operators which do not preserve $\cP_n$. We
characterize the only possible exceptional subspaces of codimension one and we
describe the space of second order differential operators that leave these
subspaces invariant. We then use equivalence under changes of variable and
gauge transformations to achieve a complete classification of these new,
non-Lie algebraic Schrodinger operators. As an example, we discuss a finite gap
elliptic potential which does not belong to the Treibich-Verdier class.


title: The Hamiltonian Structure of the Second Painleve Hierarchy

abstract:
  In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable $z$ depending on n
parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new
canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates.


title:
Reducing multiphoton ionization in a linearly polarized microwave field
  by local control

abstract:
  We present a control procedure to reduce the stochastic ionization of
hydrogen atom in a strong microwave field by adding to the original Hamiltonian
a comparatively small control term which might consist of an additional set of
microwave fields. This modification restores select invariant tori in the
dynamics and prevents ionization. We demonstrate the procedure on the
one-dimensional model of microwave ionization.


title: Hyperacceleration in a stochastic Fermi-Ulam model

abstract:
  Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of
particles bouncing between two, infinitely heavy, stochastically oscillating
hard walls, is investigated. It is shown that the widely used approximation,
neglecting the displacement of the walls (static wall approximation), leads to
a systematic underestimation of particle acceleration. An improved
approximative map is introduced, which takes into account the effect of the
wall displacement, and in addition allows the analytical estimation of the long
term behavior of the particle mean velocity as well as the corresponding
probability distribution, in complete agreement with the numerical results of
the exact dynamics. This effect accounting for the increased particle
acceleration -Fermi hyperacceleration- is also present in higher dimensional
systems, such as the driven Lorentz gas.


title:
High-Order-Mode Soliton Structures in Two-Dimensional Lattices with
  Defocusing Nonlinearity

abstract:
  While fundamental-mode discrete solitons have been demonstrated with both
self-focusing and defocusing nonlinearity, high-order-mode localized states in
waveguide lattices have been studied thus far only for the self-focusing case.
In this paper, the existence and stability regimes of dipole, quadrupole and
vortex soliton structures in two-dimensional lattices induced with a defocusing
nonlinearity are examined by the theoretical and numerical analysis of a
generic envelope nonlinear lattice model. In particular, we find that the
stability of such high-order-mode solitons is quite different from that with
self-focusing nonlinearity. As a simple example, a dipole (``twisted'') mode
soliton which may be stable in the focusing case becomes unstable in the
defocusing regime. Our results may be relevant to other two-dimensional
defocusing periodic nonlinear systems such as Bose-Einstein condensates with a
positive scattering length trapped in optical lattices.


title:
Lyapunov--Schmidt reduction algorithm for three-dimensional discrete
  vortices

abstract:
  We address persistence and stability of three-dimensional vortex
configurations in the discrete nonlinear Schr\"{o}dinger (NLS) equation and
develop a symbolic package based on Wolfram's MATHEMATICA for computations of
the Lyapunov--Schmidt reduction method. The Lyapunov--Schmidt reduction method
is a theoretical tool which enables us to study continuations and terminations
of the discrete vortices for small coupling between lattice nodes as well as
the spectral stability of the persistent configurations. The method was
developed earlier in the context of the two-dimensional NLS lattice and applied
to the on-site and off-site configurations (called the vortex cross and the
vortex cell) by using semi-analytical computations. The present treatment
develops a full symbolic computational package which takes a desired waveform
at the anti-continuum limit of uncoupled sites, performs a required number of
Lyapunov--Schmidt reductions and outputs the predictions on whether the
configuration persists, for finite coupling, in the three-dimensional lattice
and whether it is stable or unstable. It also provides approximations for the
eigenvalues of the linearized stability problem. We report a number of
applications of the algorithm to important multi-site configurations, such as
the simple cube, the double cross, and the diamond. For each three-dimensional
configuration, we identify exactly one solution, which is stable for small
coupling between lattice nodes.


title:
Pulse Dynamics in Coupled Excitable FIbers: Soliton-like Collision,
  Recombination, and Overtaking

abstract:
  We study the dynamics of a reaction-diffusion system composed of two mutually
coupled excitable fibers. We focus on the situation in which dynamical
properties of the two fibers are not identical because of the parameter
difference between the fibers. Using the spatially one-dimensional
FitzHugh-Nagumo equations as a model of a single excitable fiber, we show that
the system exhibits a rich variety of dynamical behavior, including
soliton-like collision between two pulses, recombination of a solitary pulse
and synchronized pulses, and overtaking of a slow-moving solitary pulse by
fast-moving synchronized pulses.


title: Algebraic properties of Gardner's deformations for integrable systems

abstract:
  An algebraic definition of Gardner's deformations for completely integrable
bi-Hamiltonian evolutionary systems is formulated. The proposed approach
extends the class of deformable equations and yields new integrable
evolutionary and hyperbolic Liouville-type systems. An exactly solvable
two-component extension of the Liouville equation is found.


title: Hamiltonian Structure of PI Hierarchy

abstract:
  The string equation of type $(2,2g+1)$ may be thought of as a higher order
analogue of the first Painlev\'e equation that corresponds to the case of $g =
1$. For $g > 1$, this equation is accompanied with a finite set of commuting
isomonodromic deformations, and they altogether form a hierarchy called the PI
hierarchy. This hierarchy gives an isomonodromic analogue of the well known
Mumford system. The Hamiltonian structure of the Lax equations can be
formulated by the same Poisson structure as the Mumford system. A set of
Darboux coordinates, which have been used for the Mumford system, can be
introduced in this hierarchy as well. The equations of motion in these Darboux
coordinates turn out to take a Hamiltonian form, but the Hamiltonians are
different from the Hamiltonians of the Lax equations (except for the lowest one
that corresponds to the string equation itself).


title: Characteristic Lie Algebra and Classification of Semi-Discrete Models

abstract:
  Characteristic Lie algebras of semi-discrete chains are studied. The attempt
to adopt this notion to the classification of Darboux integrable chains has
been undertaken.


title:
Hamiltonian curve flows in Lie groups $G\subset U(N)$ and vector NLS,
  mKdV, sine-Gordon soliton equations

abstract:
  A bi-Hamiltonian hierarchy of complex vector soliton equations is derived
from geometric flows of non-stretching curves in the Lie groups
$G=SO(N+1),SU(N)\subset U(N)$, generalizing previous work on integrable curve
flows in Riemannian symmetric spaces $G/SO(N)$. The derivation uses a parallel
frame and connection along the curves, involving the Klein geometry of the
group $G$. This is shown to yield the two known $U(N-1)$-invariant vector
generalizations of the nonlinear Schrodinger (NLS) equation and the complex
modified Korteweg-de Vries (mKdV) equation, as well as $U(N-1)$-invariant
vector generalizations of the sine-Gordon (SG) equation found in recent
symmetry-integrability classifications of hyperbolic vector equations. The
curve flows themselves are described in explicit form by chiral wave maps,
chiral variants of Schrodinger maps, and mKdV analogs.


title: Heat Polynomials, Umbral Correspondence and Burgers Equations

abstract:
  We show that the umbral correspondence between differential equations can be
achieved by means of a suitable transformation preserving the algebraic
structure of the problems. We present the general properties of these
transformations, derive explicit examples and discuss them in the case of the
App\`{e}l and Sheffer polynomial families. We apply these transformations to
non-linear equations, and discuss how the relevant solutions should be
interpreted.


title: Dynamics of the Cellular Automaton Rule 142

abstract:
  We investigate dynamics of the cellular automaton rule 142. This rule
possesses additive invariant of the second order, namely it conserves the
number of blocks 10. Rule 142 can be alternatively described as an operation on
a binary string in which we simultaneously flip all symbols which have
dissenting right neighbours. We show that the probability of having a
dissenting neighbour can be computed exactly using the fact that the surjective
rule 60 transforms rule 142 into rule 226. We also demonstrate that the
conservation of the number of 10 blocks implies that these blocks move with
speed -1 or stay in the same place, depending on the state of the preceding
site. At the density of blocks 10 equal to 0.25, the rule 142 exhibits a
phenomenon similar to the jamming transitions occurring in discrete models of
traffic flow.


title:
Critical behavior of number-conserving cellular automata with nonlinear
  fundamental diagrams

abstract:
  We investigate critical properties of a class of number-conserving cellular
automata (CA) which can be interpreted as deterministic models of traffic flow
with anticipatory driving. These rules are among the only known CA rules for
which the shape of the fundamental diagram has been rigorously derived. In
addition, their fundamental diagrams contain nonlinear segments, as opposed to
majority of number-conserving CA which exhibit piecewise-linear diagrams. We
found that the nature of singularities in the fundamental diagram of these
rules is the same as for rules with piecewise-linear diagrams. The current
converges toward its equilibrium value like $t^{-1/2}$, and the critical
exponent $\beta$ is equal to 1. This supports the conjecture of universal
behavior at singularities in number-conserving rules. We discuss properties of
phase transitions occurring at singularities as well as properties of the
intermediate phase.


title:
The unfair consequences of equal opportunities: comparing exchange
  models of wealth distribution

abstract:
  Simple agent based exchange models are a commonplace in the study of wealth
distribution of artificial societies. Generally, each agent is characterized by
its wealth and by a risk-aversion factor, and random exchanges between agents
allow for a redistribution of the wealth. However, the detailed influence of
the amount of capital exchanged has not been fully analyzed yet. Here we
present a comparison of two exchange rules and also a systematic study of the
time evolution of the wealth distribution, its functional dependence, the Gini
coefficient and time correlation functions. In many cases a stable state is
attained, but, interesting, some particular cases are found in which a very
slow dynamics develops. Finally, we observe that the time evolution and the
final wealth distribution are strongly dependent on the exchange rules in a
nontrivial way.


title: Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model

abstract:
  The problem of magnetic vortex dynamics in an anisotropic spin liquid model
is considered. For incompressible flow the model admits reduction to saturating
Bogomolny inequality analytic projections of spin variables, subject the linear
holomorphic Schr\"odinger equation. It allows us to construct N vortex
configurations in terms of the complex Hermite polynomials. Using complex
Galilean boost transformations, the interaction of the vortices and the vortex
chain lattices (vortex crystals) are studied. By the complexified Cole-Hopf
transformation, integrable N vortex dynamics is described by the holomorphic
Burgers equation. Mapping of the point vortex problem to N-particle problem,
the complexified Calogero-Moser system, showing its integrability and the
Hamiltonian structure, is given.


title:
Solitons of the Resonant Nonlinear Schrodinger Equation with Nontrivial
  Boundary Conditions and Hirota Bilinear Method

abstract:
  Physically relevant soliton solutions of the resonant nonlinear Schrodinger
(RNLS) equation with nontrivial boundary conditions, recently proposed for
description of uniaxial waves in a cold collisionless plasma, are considered in
the Hirota bilinear approach. By the Madelung representation, the model is
transformed to the reaction-diffusion analog of the NLS equation for which the
bilinear representation, soliton solutions and their mutual interactions are
studied.


title: Solitons in strongly driven discrete nonlinear Schr\"odinger-type models

abstract:
  Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear
Schr\"odinger (DNLS) equations with damping and strong rapid drive are
investigated. The averaged equations have the forms of the parametric AL and
DNLS equations. A new type of parametric bright discrete soliton and cnoidal
waves are found and the stability properties are analyzed. The analytical
predictions of the perturbed inverse scattering transform are confirmed by the
numerical simulations of the AL and DNLS equations with rapidly varying drive
and damping.


title:
Mathematical modeling of pattern formation in sub- and supperdiffusive
  reaction-diffusion systems

abstract:
  This paper is concerned with analysis of coupled fractional
reaction-diffusion equations. It provides analytical comparison for the
fractional and regular reaction-diffusion systems. As an example, the
reaction-diffusion model with cubic nonlinearity and Brusselator model are
considered. The detailed linear stability analysis of the system with Cubic
nonlinearity is provided. It is shown that by combining the fractional
derivatives index with the ratio of characteristic times, it is possible to
find the marginal value of the index where the oscillatory instability arises.
Computer simulation and analytical methods are used to analyze possible
solutions for a linearized system. A computer simulation of the corresponding
nonlinear fractional ordinary differential equations is presented. It is shown
that the increase of the fractional derivative index leads to the periodic
solutions which become stochastic at the index approaching the value of 2. It
is established by computer simulation that there exists a set of stable
spatio-temporal structures of the one-dimensional system under the Neumann and
periodic boundary condition. The characteristic features of these solutions
consist in the transformation of the steady state dissipative structures to
homogeneous oscillations or space temporary structures at a certain value of
fractional index.


title: The nxn KdV flows

abstract:
  We introduce a new integrable system hierarchy which is a restriction of the
AKNS nxn hierarchy coming from an unusual splitting of the loop algebra. This
splitting comes from an automorphism of the loop algebra instead of an
automorphism of SL(n,C). It is known that the 2x2 KdV is the standard KdV
hierarchy.


title:
Change in the adiabatic invariant in a nonlinear two-mode model of
  Feshbach resonance passage

abstract:
  Mean-field approach has recently been used to model coupled atom-molecular
Bose-Einstein condensates (BEC) and coupled Fermi-Bose condensates near
Feshbach resonance. Sweeping of magnetic field across the resonance gives a new
(nonlinear) version of Landau-Zener problem. We investigate the structure of
the corresponding classical phase space and calculate change in the action
which corresponds to finite-rate efficiency of the sweep. We consider the case
of non-zero initial action, which corresponds to some finite initial molecular
fraction.


title:
Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range
  Interaction Potentials

abstract:
  We review some recent results on quasi-exactly solvable spin models
presenting near-neighbors interactions. These systems can be understood as
cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial
modification of the exchange operator formalism is used to obtain several
infinite families of eigenfunctions of these models in closed form.


title:
Rational soliton on the plane wave background for the (1+2)
  $|\phi|^4$-model with negative coupling

abstract:
  We show that $(1+2)$ nonlinear Klein-Gordon equation with negative coupling
admits an exact solution which appears to be the linear superposition of the
plane wave and the nonsingular rational soliton.


title:
Anticipation of summer monsoon rainfall over India by Artificial Neural
  Network with Conjugate Gradient Descent Learning

abstract:
  Present study aims to develop a predictive model for the average summer
monsoon rainfall amount over India. The dataset made available by the Indian
Institute of Tropical Meteorology, Pune, has been explored. To develop the
predictive model, Backpropagation method with Conjugate Gradient Descent
algorithm has been implemented. The Neural Net model with the said algorithm
has been learned thrice to reach a good result. After three runs of the model,
it is found that a high prediction yield is available. Ultimately, Artificial
Neural Network with Conjugate Gradient Descent based Backpropagation algorithm
is found to be skillful in predicting average summer monsoon rainfall amount
over India.


title: Stimulated Raman Transfer of SIT Solitons

abstract:
  We treat theoretically the two-pulse plane-wave propagation problem
associated with the stimulated Raman process. A strong pump pulse and a weak
probe pulse interact self-consistently during mutual propagation through a
medium in the three-level lambda configuration. We treat the pulse interaction
fully coherently, but take initially incoherent mixed ground states to describe
the medium. We present analytic pulse envelope solutions to the nonlinear
evolution equations, and then test them numerically. We show that the entire
process can be interpreted consistently as a three-regime evolution, in which
the first and last regimes display behavior quantitatively the same as
self-induced transparency. They are connected through a Raman transfer process
in the intermediate regime.


title:
Collisions of a light bullet with kinks and standing breathers in the
  two-dimensional sine-Gordon equation

abstract:
  The (2+1)-dimension Klein-Gordon generalised equation is numerically solved
through the finite differences method. Only the sine-Gordon case is focused:
kink and antikink solutions are obtained in cartesian coordinates and evidence
of interaction in kink-kink collision is looked for in propagation velocity.
Then the change of shape in light bullet solutions is quantified during
propagation and in head-on collision. Lastly, the robustness of light bullets
is verified in head-on collisions with kink, antikink, standing kink and
standing breather. A 30o-collision between a light bullet and a standing kink
is simulated as well.


title:
Rational expansion method of exponent function for solving exact
  solutions to nonlinear differential-difference equations

abstract:
  A new method named rational expansion method of exponent function is
presented to find exact traveling wave solutions of differential-difference
equations. This method generalizes the so-called tanh-method and other similar
methods. Some examples are dealt with and their abundant exact solutions which
include solitary solutions and periodic solutions are obtained. Among them,
many solutions are new.


title: Generalized Lattice Boltzmann Method with multi-range pseudo-potential

abstract:
  The physical behaviour of a class of mesoscopic models for multiphase flows
is analyzed in details near interfaces. In particular, an extended
pseudo-potential method is developed, which permits to tune the equation of
state and surface tension independently of each other. The spurious velocity
contributions of this extended model are shown to vanish in the limit of high
grid refinement and/or high order isotropy. Higher order schemes to implement
self-consistent forcings are rigorously computed for 2d and 3d models. The
extended scenario developed in this work clarifies the theoretical foundations
of the Shan-Chen methodology for the lattice Boltzmann method and enhances its
applicability and flexibility to the simulation of multiphase flows to density
ratios up to O(100).

categories: nlin.CG cond-mat.stat-mech nlin.CD physics.comp-ph


title: Nonperiodic echoes from mushroom billiard hats

abstract:
  Mushroom billiards have the remarkable property to show one or more clear cut
integrable islands in one or several chaotic seas, without any fractal
boundaries. The islands correspond to orbits confined to the hats of the
mushrooms, which they share with the chaotic orbits. It is thus interesting to
ask how long a chaotic orbit will remain in the hat before returning to the
stem. This question is equivalent to the inquiry about delay times for
scattering from the hat of the mushroom into an opening where the stem should
be. For fixed angular momentum we find that no more than three different delay
times are possible. This induces striking nonperiodic structures in the delay
times that may be of importance for mesoscopic devices and should be accessible
to microwave experiments.

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


title:
Elastic and inelastic line-soliton solutions of the
  Kadomtsev-Petviashvili II equation

abstract:
  The Kadomtsev-Petviashvili II (KPII) equation admits a large variety of
multi-soliton solutions which exhibit both elastic as well as inelastic types
of interactions. This work investigates a general class of multi-solitons which
were not previously studied, and which do not in general conserve the number of
line solitons after interaction. The incoming and outgoing line solitons for
these solutions are explicitly characterized by analyzing the $\tau$-function
generating such solutions. A special family of $N$-soliton solutions is also
considered in this article. These solutions are characterized by elastic
soliton interactions, in the sense that amplitude and directions of the
individual line solitons as $y\to\infty$ are the same as those of the
individual line solitons as $y\to-\infty$. It is shown that the solution space
of these elastic $N$-soliton solutions can be classified into $(2N-1)!!$
disjoint sectors which are characterized in terms of the amplitudes and
directions of the $N$ line solitons.


title:
Cryptanalysis of two chaotic encryption schemes based on circular bit
  shift and XOR operations

abstract:
  Recently two encryption schemes were proposed by combining circular bit shift
and XOR operations, under the control of a pseudorandom bit sequence (PRBS)
generated from a chaotic system. This paper studies the security of these two
encryption schemes and reports the following findings: 1) there exist some
security defects in both schemes; 2) the underlying chaotic PRBS can be
reconstructed as an equivalent key by using only two chosen plaintexts; 3) most
elements in the underlying chaotic PRBS can be obtained by a differential
known-plaintext attack using only two known plaintexts. Experimental results
are given to demonstrate the feasibility of the proposed attack.


title: Generalized isothermic lattices

abstract:
  We study multidimensional quadrilateral lattices satisfying simultaneously
two integrable constraints: a quadratic constraint and the projective Moutard
constraint. When the lattice is two dimensional and the quadric under
consideration is the Moebius sphere one obtains, after the stereographic
projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by
an algebraic constraint imposed on the (complex) cross-ratio of the circular
lattice. We derive the analogous condition for our generalized isthermic
lattices using Steiner's projective structure of conics and we present basic
geometric constructions which encode integrability of the lattice. In
particular, we introduce the Darboux transformation of the generalized
isothermic lattice and we derive the corresponding Bianchi permutability
principle. Finally, we study two dimensional generalized isothermic lattices,
in particular geometry of their initial boundary value problem.


title: Integrability conditions for nonautonomous quad-graph equations

abstract:
  This paper presents a systematic investigation of the integrability
conditions for nonautonomous quad-graph maps, using the Lax pair approach, the
ultra-local singularity confinement criterion and direct construction of
conservation laws. We show that the integrability conditions derived from each
of the methods are the one and the same, suggesting that there exists a deep
connection between these techniques for partial difference equations.


title: Construction of Integrals of Higher-Order Mappings

abstract:
  We find that certain higher-order mappings arise as reductions of the
integrable discrete A-type KP (AKP) and B-type KP (BKP) equations. We find
conservation laws for the AKP and BKP equations, then we use these conservation
laws to derive integrals of the associated reduced maps.


title: On the Dynamics of Navier-Stokes and Euler Equations

abstract:
  This is a rather comprehensive study on the dynamics of Navier-Stokes and
Euler equations via a combination of analysis and numerics. We focus upon two
main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes
operator, (b). heteroclinics conjecture for Euler equation, its numerical
verification, Melnikov integral, and simulation and control of chaos. Besides
Navier-Stokes and Euler equations, we also study two models of them.

categories: nlin.CD math-ph math.AP math.MP physics.flu-dyn


title:
Modified dispersionless Veselov--Novikov equations and corresponding
  hydrodynamic chains

abstract:
  Various links connecting well-known hydrodynamic chains and corresponding 2+1
nonlinear equations are described.