A family of the Poisson brackets compatible with the Sklyanin bracket

Details A family of the Poisson brackets compatible with the Sklyanin bracket A family of the Poisson brackets compatible with the Sklyanin bracket

2006-12-12

arxiv.org/abs/nlin/0612025v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, LaTeX with Amsfonts; corrected typos

Scientific paper

We introduce a family of compatible Poisson brackets on the space of $2\times
2$ polynomial matrices, which contains the Sklyanin bracket, and use it to
derive a multi-Hamiltonian structure for a set of integrable systems that
includes $XXX$ Heisenberg magnet, the open and periodic Toda lattices, the
discrete self-trapping model and the Goryachev-Chaplygin gyrostat.

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