摘要:

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 Hamiltonian structure of the systems in a complete symmetry class are described. If such a system has a degenerate characteristic speed, then it has conservation laws of arbitrarily high order. Symmetry classes of 2-component hyperbolic systems correspond to coframes on the plane. The invariants of 2-component Hamiltonian hyperbolic symmetry classes are given. An exact symmetry class of 2-component hyperbolic systems is characterized by its canonical representative, and the first order conservation laws of the canonical system correspond to the infinitesimal automorphisms of the coframe. The normal forms of the rank 0 and rank 1 exact classes are listed. A simple symmetry class is tri-Hamiltonian if and only if the metric of its coframe has constant curvature. The normal forms of the tri-Hamiltonian simple classes are listed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.3.1

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

CoupledKdVequations 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 modified equations. A second set of Miura transformation can also be generated leading to complicated form of coupled integrable systems.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.3.2

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

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 the whole hierarchy and construct the associated linearr-matrix algebra with ther-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Classical integration in a particular case is carried out and quantization of the system is discussed with the help of separation variables.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.3.3

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We study representations of the generalized Poincaré group and its extensions in the class of Lie vector fields acting in a space ofn+mindependent and one dependent variables. We prove that an arbitrary representation of the groupP(n, m) with max {n, m} ≥ 3 is equivalent to the standard one, while the conformal groupC(n, m) has non-trivial nonlinear representations. Besides that, we investigate in detail representations of the Poincaré groupP(2, 2), extended Poincaré groups,, and conformal groupsC(1, 2),C(2, 2) and obtain their linear and nonlinear representations.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.3.4

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

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 1-forms. After multiplying this system by a set of multiplicative functions, we demand the existence of first integrals. More interesingly these multipliers play a crucial role in constructing the required Poisson structures, if it exists. We illustrate this procedure with a class of physically interesting systems.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.3.5

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor