Linear r-matrix algebra for classical separable systems

J. C. Eilbeck, V. Z. Enol'skii, V. B. Kuznetsov, A. V. Tsiganov

Research output: Contribution to journalArticle

Abstract

We consider a hierarchy of the natural-type Hamiltonian systems of n degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. 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. Using the method of variable separation, we provide the integration of the systems in classical mechanics constructing the separation equations and, hence, the explicit form of action variables. The quantization problem is discussed with the help of the separation variables.

Original languageEnglish
Article number038
Pages (from-to)567-578
Number of pages12
JournalJournal of Physics A: Mathematical and General
Volume27
Issue number2
DOIs
Publication statusPublished - 1994

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