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A family of the Poisson brackets compatible with the Sklyanin bracket

A. V. Tsiganov
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Abstract

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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A. V. Tsiganov. 2007-03-10. A family of the Poisson brackets compatible with the Sklyanin bracket. https://doi.org/10.1088/1751-8113%2F40%2F18%2F008

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