Volume 8, Issue Supplement, February 2001

Pages: 1 - 4

We propose Dirac formalism for constraint Hamiltonian systems as an useful tool
for the algebro-geometrical and dynamical characterizations of a class of integrable
systems, the so called hyperelliptically separable systems. As a model example, we
apply it to the classical geodesic flow on an ellipsoid.

Pages: 5 - 12

Solitons of the parametrically driven, damped nonlinear Schrödinger equation become
unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We
show that the chaos can be suppressed by introducing localized inhomogeneities in
the parameters of the equation. The pinning of...

Pages: 13 - 17

The suq(2) algebra is shown to provide a natural dynamical algebra for some nonlnear models in Quantum Optics. Applications to the computation of eigenvalues and
eigenvectors for the Hamiltonian describing second harmonics generation are proposed.

Pages: 18 - 22

The two-photon algebra h6 is used to define an infinite class of N-particle Hamiltonian
systems having (N -2) additional constants of the motion in involution. By constrution, all these systems are h6-coalgebra invariant. As a straightforward application, a
new family of (quasi)integrable N-dimensional...

Pages: 23 - 27

Explicit formulas are given for the multi-peakon-antipeakon solutions of the Camassa
Holm equation, and a detailed analysis is made of both short-term and long-term
aspects of the interaction between a single peakon and single anti-peakon.

Pages: 28 - 34

Dynamics of spiral waves in perturbed two-dimensional autowave media can be dscribed asymptotically in terms of Aristotelean dynamics. We apply this general thory to the spiral waves in the Complex GinzburgLandau equation (CGLE). The RFs
are found numerically. In this work, we study the dependence...

Pages: 35 - 41

In this brief contribution, which is based on my talk at the conference, I discuss the
dynamics of solutions of nonlinear wave equations near the threshold of singularity
formation. The heuristic picture of threshold behavior is first presented in a general
setting and then illustrated with three...

Pages: 42 - 47

The gauge-field theoretical formulation of solitonic theories is quantized by using an
extended version of the BRST Sp(2) symmetric formalism. The proposed method
is based on a modified triplectic geometry which allows us to incorporate the linear
and/or nonlinear global symmetries of the model and...

Pages: 48 - 52

Extending the gauge-invariance principle for functions of the standard bilinear fomalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators.
Using them, we bilinearize SUSY KdV equation. The solution for multiple collisions
of super-solitons is given.

Pages: 53 - 57

A reduction process to construct hidden hierarchies corresponding to the Gelfand
Dickey ones is outlined in a specific example, not yet treated in the literature.

Pages: 58 - 61

In this article, we present an explicit linearization of dynamical systems of RuijsenaarSchneider (RS) type and of the perturbations introduced by F Calogero [2] of these
systems with all orbits periodic of the same period. The existence of this linearization
and its algebraic nature relies on the...

Pages: 62 - 68

We exhibit a class of Dirac operators that possess Huygens' property, i.e., the support
of their fundamental solutions is precisely the light cone. This class is obtained by
considering the rational solutions of the modified Korteweg-de Vries hierarchy.

Pages: 69 - 78

We review the construction of Lax pairs with spectral parameter for twisted and utwisted elliptic Calogero-Moser systems defined by a general simple Lie algebra G, and
the corresponding solution of N = 2 SUSY G Yang-Mills theories with a hypermultplet in the adjoint representation of G.

Pages: 79 - 81

We consider the following question: Suppose part of the boundary of a cavity contaiing a gas is set into oscillation, the damping in the boundary being small. What is the
nature of the oscillations in the gas? We treat the low-frequency limit (wavelength
much greater than dimensions of the cavity)....

Pages: 82 - 87

We study statistical properties of inhomogeneous Burgers lattices which are solved by
the discrete ColeHopf transformation. Using exact solutions we investigate effect of
various kinds of noise on the dynamics of solutions.

Pages: 88 - 92

The asymptotic lattices and their transformations are included into the theory of
quadrilateral lattices.

Pages: 93 - 99

A method of quantization of classical soliton cellular automata (QSCA) is put forward
that provides a description of their time evolution operator by means of quantum cicuits that involve quantum gates from which the associated Hamiltonian describing
a quantum chain model is constructed. The intrinsic...

Pages: 100 - 105

Brownian motion on a smash line algebra (a smash or braided version of the algebra
resulting by tensoring the real line and the generalized paragrassmann line algebras),
is constructed by means of its Hopf algebraic structure. Further, statistical moments,
non stationary generalizations and its diffusion...

Pages: 106 - 111

The real version of a (2 + 1) dimensional integrable generalization of the nonlinear
Schrödinger equation is studied from the point of view of Painlevé analysis. In this
way we find the Lax pair, Darboux transformations and Hirota's functions as well as
solitonic and dromionic solutions from an iterative...

Pages: 112 - 117

We analyse timing jitter of ultrashort soliton systems taking into account the major
higher order effects, namely, intrapulse Raman scattering and third order dispersion
and using adiabatic perturbation theory. We obtain an expression for the soliton
arrival time variance that depends on the quintic...

Pages: 118 - 127

We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using
some recent results on the separation of variables for bihamiltonian manifold, we
show that these systems can be explicitly integrated via the classical HamiltonJacobi
method in the so-called DarbouxNijenhuis coordinates.

Pages: 128 - 132

We extend a previous result, namely we show that the solution of the Whitham equtions is asymptotically self-similar for generic monotone polynomial initial data with
smooth perturbation.

Pages: 133 - 138

We prove the persistence of finite dimensional invariant tori associated with the dfocusing nonlinear Schrödinger equation under small Hamiltonian perturbations. The
invariant tori are not necessarily small.

Pages: 139 - 144

Multi-scales method is used to analyze a nonlinear differential-difference equation. In
the order 3
the NLS eq. is found to determine the space-time evolution of the leading
amplitude. In the next order this has to satisfy a complex mKdV eq. (the next in the
NLS hierarchy) in order to eliminate secular...

Pages: 145 - 148

In this note, we present a result to show that the symplectic structures have been
naturally encoded into the Painlevé test. In fact, for every principal balance, there is
a symplectic change of dependent variables near movable poles.

Pages: 149 - 155

This paper shows that several integrable lattices can be transformed into coupled biliear differential-difference equations by introducing auxiliary variables. By testing the
Bäcklund transformations for this type of coupled bilinear equations, a new integrable
lattice is found. By using the Bäcklund...

Pages: 156 - 160

The Cauchy problem for the Liouville equation with a small perturbation is considered.
We are interested in the asymptotics of the perturbed solution under the assumption
that one has singularity. The main goal is to study both the asymptotic approximation
of the singular lines and the asymptotic...

Pages: 161 - 165

We introduce a nonlinear and noncanonical gauge transformation which allows the rduction of a complex nonlinearity, contained in a Schrödinger equation, into a real one.
This Schrödinger equation describes a canonical system, whose kinetics is governed by
a generalized Exclusion-Inclusion Principle....

Pages: 166 - 171

An integrable discretization of an inhomogeneous Volterra lattice is introduced. Some
aspects of dynamics of a soliton affected by a random force are discussed.

Pages: 172 - 177

An approach to the Painlevé analysis of fourth-order ordinary differential equations is
presented. Some fourth-order ordinary differential equations which pass the Painlevé
test are found.

Pages: 178 - 182

The inhomogeneity of the media or the external forces usually destroy the integrability
of a system. We propose a systematic construction of a class of quantum models, which
retains their exact integrability inspite of their explicit inhomogeneity. Such models
include variable mass sine-Gordon model,...

Pages: 183 - 187

Renormalization group flow equations for scalar 4
are generated using smooth
smearing functions. Numerical results for the critical exponent in d = 3 are caculated by polynomial truncation of the blocked potential. It is shown that the covergence of with the order of truncation can be improved by...

Pages: 188 - 194

The simple model of the non-linear DNA dynamics [4] is pursued in order to study the
local untwisting of DNA double helix. It is shown how the advancing RNA polymerase
may force the motion of the torsional solitary wave along DNA.

Pages: 195 - 199

A new class of integrable Newton systems in Rn
is presented. They are characterized
by the existence of two quadratic integrals of motion of so-called cofactor type, and are
therefore called cofactor pair systems. This class includes as special cases conservative
systems separable in elliptic or...

Pages: 200 - 206

We study the problem of non-integrability (integrability) of cosmological dynamcal systems which are given in the Hamiltonian form with indefinite kinetic energy
form T = 1
2 g(v, v), where g is a two-dimensional pseudo-Riemannian metric with a
Lorentzian signature (+, -), and v TxM is a tangent...

Pages: 207 - 211

A dispersionless integrable system with repeated eigenvalues is presented. For N 3
components the system has no local Hamiltonian structure. Infinitely many simple
compatible non-local Hamiltonian structures are given, using a result of Ferapontov.

Pages: 212 - 218

The Laplacian growth problem in the limit of zero surface tension is proved to be
equivalent to finding a particular solution to the dispersionless Toda lattice hierarchy.
The hierarchical times are harmonic moments of the growing domain. The Laplacian
growth equation itself is the quasiclassical...

Pages: 219 - 224

In the present work we discuss arguments in favour of the view that massive fermions
represent dislocations (i.e. topological solitons) in discrete space-time, with Burgers
vectors parallel to the axis of time. If we assume that the symmetrical parts of
tensors of distortions (i.e. derivatives of...

Pages: 225 - 229

An influence of the quantum potential on the ChernSimons solitons leads to quatization of the statistical parameter = me2
/g, and the quantum potential strenght
s = 1 - m2
. A new type of exponentially localized ChernSimons solitons for the
Bloch electrons near the hyperbolic energy band boundary...

Pages: 230 - 234

The reaction-diffusion system realizing a particular gauge fixing condition of the
JackiwTeitelboim gravity is represented as a coupled pair of Burgers equations with
positive and negative viscosity. For acoustic metric in the Madelung fluid representtion the space-time points where dispersion change...

Pages: 235 - 239

The BBGKY's chain of quantum kinetic equations that describes the system of Bose
particles interacting by delta potential is solved by the operator method with the help
of nonlinear Schrödinger's equations. The solution of the chain is defined in terms of
the Bethe ansatz.

Pages: 240 - 248

We present a scenario concerning the existence of a large class of reflectionless seladjoint analytic difference operators. In order to exemplify this scenario, we summarize
our results on reflectionless self-adjoint difference operators of relativistic CalogerMoser type.

Pages: 249 - 253

We use Lax equations to define a scattering problem on an infinite elbow shaped line
of the (x, t) plane. The evolution of scattering coefficients when the elbow is translated
in the plane shows how convenient scannings may reconstruct the solution V (x, t) of
the nonlinear equation associated to...

Pages: 254 - 260

In this talk we introduce generalised CalogeroMoser models and demonstrate their
integrability by constructing universal Lax pair operators. These include models based
on non-crystallographic root systems, that is the root systems of the finite reflection
groups, H3, H4, and the dihedral group I2(m),...

Pages: 261 - 265

We consider the following spectral problem
y1
y2 x
=
-w u
v w
y1
y2
M
y1
y2
, (1)
where u, v, w are smooth functions. It produces a hierarchy of evolution equations
with an arbitrary function Am-1. This hierarchy includes the WKI [8] and Heiseberg [7] hierarchies by properly selecting...

Pages: 266 - 271

In the paper we analyze the KaldorKalecki model of business cycle. The time dlay is introduced to the capital accumulation equation according to Kalecki's idea of
delay in investment processes. The dynamics of this model is represented in terms
of time delay differential equation system. In the special...

Pages: 272 - 277

First of all, we show the existence of the Lax pair for the Calogero Korteweg-de
Vries(CKdV) equation. Next we modify T operator that is one of the Lax pair for
the CKdV equation for the search of the (2 + 1)-dimensional case and propose a new
equation in (2 + 1) dimensions. We call it the (2 + 1)-dimensional...

Pages: 278 - 282

For the Toda lattice we consider properties of the canonical transformations of the
extended phase space, which preserve integrability. At the special values of integrals
of motion the integral trajectories, separated variables and the action variables are
invariant under change of the time. On the...

Pages: 283 - 288

The compatible expansion in series of solutions of both the equations of PQ pair at
neighborhood of the singular point is obtained in closed form for regular and irregular
singularities. The conservation laws of the system of ordinary differential equations
to arise from the compatibility condition...

Pages: 289 - 293

A description of the most accurate analytical theory of the motion of Phobos, so
far constructed, is presented. Several elements of the gravitational field of Mars,
gravitational interactions between Phobos and Mars, Deimos and Jupiter, as well
as tidal effects due to the interaction between the Sun...

Pages: 294 - 299

An integrable interpolative (Pivotal) model for the (1 + 1)-dimensional Hyperbolic
Heisenberg and Hyperbolic sigma models is proposed and some solutions classifiable
by an integer winding number examined.

Pages: 300 - 304

An infinite number of families of quasi-bi-Hamiltonian (QBH) systems can be costructed from the constrained flows of soliton equations. The Nijenhuis coordinates
for the QBH systems are proved to be exactly the same as the separation variables
introduced by the Lax matrices for the constrained flows.

Pages: 305 - 311

We investigate influence of mobility of neighbouring chains on dynamics of soliton-like
excitations in a chain of the simplest polymer crystal (polyethylene in the "united
atoms" approximation) using molecular dynamics simulation. We present results for
point-like structural defects: static and moving...