Journal of Nonlinear Mathematical Physics

Volume 1, Issue 3, August 1994

1. Symmetry Classes of Quasilinear Systems in One Space Variable

Philip W. DOYLE
Pages: 225 - 266
The family of simple quasilinear systems in one space variable is partitioned into classes of commuting flows, i.e., symmetry classes. The systems in a symmetry class have the same zeroth order conserved densities and the same Hamiltonian structure. The zeroth and first order conservation laws and the...

2. Homogeneous Manifold, Loop Algebra, Coupled KdV System and Generalised Miura Transformation

I. MUKHOPADHYA, A. Roy CHOWDHURY
Pages: 267 - 274
Coupled KdV equations are deduced by considering the homogeneous manifold corresponding to the homogeneous Heisenberg subalgebra of the Loop group (L(S1 , SL(2, C)). Utilisation of Birkhoff decomposition and further subalgebra consideration leads to a new generalised form of Miura map and two sets of...

3. Classical Poisson Structure for a Hierarchy of One­Dimensional Particle Systems Separable in Parabolic Coordinates

J.C. EILBECK, V.Z. ENOL'SKII, V.B. KUZNETSOV, D.V. LEYKIN
Pages: 275 - 294
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an integrable case of the Hénon-Heiles system. We give a Lax representation in terms of 2 × 2 matrices for...

4. On Linear and Non-Linear Representations of the Generalized Poincaré Groups in the Class of Lie Vector Fields

Wilhelm FUSHCHYCH, Renat ZHDANOV, Victor LAHNO
Pages: 295 - 308
We study representations of the generalized Poincaré group and its extensions in the class of Lie vector fields acting in a space of n + m independent and one dependent variables. We prove that an arbitrary representation of the group P(n, m) with max {n, m} 3 is equivalent to the standard one, while...

5. Direct Method of Finding First Integrals of Finite Dimensional Systems and Construction of Nondegenerate Poisson Structures

A. ANNAMALAI, K.M. TAMIZHMANI
Pages: 309 - 330
We present a novel method of finding first integrals and nondegenerate Poisson structures for a given system. We consider the given system as a system of differential