Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models

V. V. Sokolov; A. V. Tsiganov

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arXiv · nlin/0112011

Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models

V. V. Sokolov·A. V. Tsiganov

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Abstract

A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the Sklyanin bracket. Using different representations of the bracket, we find some integrable models and a separation of variables for them. The models obtained are deformations of known integrable systems like the Goryachev-Chaplygin top, the Toda lattice and the Heisenberg model.

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BibTeX RIS

V. V. Sokolov, A. V. Tsiganov. 2001-12-08. Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models. https://arxiv.org/abs/nlin/0112011

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