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Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates

J C Eilbeck·V Z Enol'skii·V B Kuznetsov·D V Leykin
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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 $2\times 2$ 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. This paper was published in the rary issues: Sfb 288 Preprint No. 110, Berlin and Nonlinear Mathematical Physics, {\bf 1(3)}, 275-294 (1994)

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J C Eilbeck, V Z Enol'skii, V B Kuznetsov, D V Leykin. 1998-09-02. Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates. https://arxiv.org/abs/solv-int/9809008

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