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

DOI

10.2991/jnmp.1994.1.3.3How to use a DOI?

Abstract

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 linear r-matrix algebra with the r-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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - J.C. Eilbeck
AU  - V.Z. Enol'skii
AU  - V.B. Kuznetsov
AU  - D.V. Leykin
PY  - 1994
DA  - 1994/08/01
TI  - Classical Poisson Structure for a Hierarchy of One­Dimensional Particle Systems Separable in Parabolic Coordinates
JO  - Journal of Nonlinear Mathematical Physics
SP  - 275
EP  - 294
VL  - 1
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1994.1.3.3
DO  - 10.2991/jnmp.1994.1.3.3
ID  - Eilbeck1994
ER  -