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Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models

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Abstract

We construct hierarchies of commutative Poisson subalgebras for Sklyanin brackets. Each of the subalgebras is generated by a complete set of integrals in involution. Some new integrable systems and schemes for separation of variables for them are elaborated using various well-known representations of the brackets. The constructed models include deformations for the Goryachev–Chaplygin top, the Toda chain, and the Heisenberg model.

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Authors and Affiliations

  1. Landau Institute of Theoretical Physics, Moscow, Russia

    V. V. Sokolov

  2. St. Petersburg State University, St. Petersburg, Russia

    A. V. Tsiganov

Authors
  1. V. V. Sokolov
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  2. A. V. Tsiganov
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Sokolov, V.V., Tsiganov, A.V. Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models. Theoretical and Mathematical Physics 133, 1730–1743 (2002). https://doi.org/10.1023/A:1021326727968

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  • DOI: https://doi.org/10.1023/A:1021326727968

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