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

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

2001-12-08

arxiv.org/abs/nlin/0112011v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, LaTeX with amssymb

Scientific paper

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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