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A family of the Poisson brackets compatible with the Sklyanin bracket | A. V. Tsiganov
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12 Dec 2006 | Subject: | Exactly Solvable and Integrable Systems | Abstract: | We introduce a family of compatible Poisson brackets on the space of $2 imes 2$ 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. | Source: | arXiv, nlin/0612025 | Services: | Forum | Review | PDF | Favorites |
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