摘要:

If we are given a smooth differential operator in the variablex ∈R/2πZ, 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 family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced Diff(S1)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced Diff(S1)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.1

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

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.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.2

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Explicit algebraic relations between the quantum integrals of the elliptic Calogero– Moser quantum problems related to the root systemsA2andB2are found.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.3

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

If a classicalr-matrixris skewsymmetric, its quantizationRcan lose the skewsymmetry property. Even whenRis skewsymmetric, it may not be unique.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.4

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we discuss a universal integrable model, given by a sum of two Wess-Zumino-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 for free fermions on a torus with nontrivial boundary conditions. It is universal in the sense that all other known integrable models can be derived as reductions of this model. Hence our motivation is to present an unified description of different integrable models. We present a proof of this universal action from the action of the trivial dynamical system on the cotangent bundles of the loop group. We also present some examples of reductions.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.5

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

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, harmonic and separable types of solutions, are proposed. A technique for reduction of the Weierstrass-Enneper system to decoupled linear equations, by subjecting it to certain differential constraints, is presented as well. New elementary and doubly periodic solutions are found, among them kinks, bumps and multi-soliton solutions.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.6

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

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 saddles and to sources with both real and complex eigenvalues. We demonstrate the procedure and the subsequent control on a variety of maps. We evaluate the control by examining the basins of attraction of the relevant controlled systems graphically and in some cases analytically.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.7

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We propose a hamiltonian formulation of theN= 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 ofN= 2 KdV hierarchies is recovered. We also give an easy construction of Wronskian solutions of the KP and KdV type equations.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.8

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

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.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.3.9

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor