Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 8, Issue Supplement, February 2001

Proceedings of the 13th Workshop NEEDS'99: Nonlinear Evolution Equations and Dynamical Systems

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: 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: 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: 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...
Demosthenes ELLINAS, Ioannis TSOHANTJIS
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...
Gregorio FALQUI, Franco MAGRI, Marco PEDRONI
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.
Jishan HU, Min YAN
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.
Xing-Biao HU, Hon-Wah TAM
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...
Sen-Ben LIAO
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: 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...
Oktay K PASHAEV, Jyh-Hao LEE
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...
Oktay K PASHAEV, Jyh-Hao LEE
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: 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),...
Kouichi TODA, Song-Ju YU
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...
Piotr WAZ
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...
Yunbo ZENG
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.