Journal of Nonlinear Mathematical Physics

Volume 6, Issue 3, August 1999
Research Article

1. Versal Deformations of a Dirac Type Differential Operator

Anatoliy K. Prykarpatsky, Denis Blackmore
Pages: 246 - 254
If we are given a smooth differential operator in the variable x R/2Z, its normal form, as is well known, is the simplest form obtainable by means of the Diff(S1 )-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal...
Research Article

2. Coupled KdV Equations of Hirota-Satsuma Type

S.Yu. Sakovich
Pages: 255 - 262
It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlevé test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown.
Research Article

3. Algebraic Spectral Relations for Elliptic Quantum Calogero-Moser Problems

L.A. Khodarinova, I.A. Prikhodsky
Pages: 263 - 268
Explicit algebraic relations between the quantum integrals of the elliptic Calogero­ Moser quantum problems related to the root systems A2 and B2 are found.
Short Communication

4. Remarks on Quantization of Classical r-Matrices

Boris A. Kupershmidt
Pages: 269 - 272
If a classical r-matrix r is skewsymmetric, its quantization R can lose the skewsymmetry property. Even when R is skewsymmetric, it may not be unique.
Research Article

5. Quest for Universal Integrable Models

Partha Guha
Pages: 273 - 293
In this paper we discuss a universal integrable model, given by a sum of two WessZumino-Witten-Novikov (WZWN) actions, corresponding to two different orbits of the coadjoint action of a loop group on its dual, and the Polyakov-Weigmann cocycle describing their interactions. This is an effective action...
Research Article

6. On Certain Classes of Solutions of the Weierstrass-Enneper System Inducing Constant Mean Curvature Surfaces

P. Bracken, A.M. Grundland
Pages: 294 - 313
Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing certain classes of solutions to this system, including potential,...
Research Article

7. Viewing the Efficiency of Chaos Control

Philippe Chanfreau, Hannu Lyyjynen
Pages: 314 - 331
This paper aims to cast some new light on controlling chaos using the OGY- and the Zero-Spectral-Radius methods. In deriving those methods we use a generalized procedure differing from the usual ones. This procedure allows us to conveniently treat maps to be controlled bringing the orbit to both various...
Research Article

8. A Note on the Third Family of N = 2 Supersymmetric KdV Hierarchies

F. Delduc, L. Gallot
Pages: 332 - 343
We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered. We...
Research Article

9. Coadjoint Poisson Actions of Poisson-Lie Groups

Boris A. Kupershmidt, Ognyan S. Stoyanov
Pages: 344 - 354
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra induces on it a non-trivial class of quadratic Poisson structures extending the linear Poisson bracket on the coadjoint orbits.