Theoretical and Mathematical Physics

, Volume 133, Issue 3, pp 1730–1743 | Cite as

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

  • V. V. Sokolov
  • A. V. Tsiganov
Article

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.

finite-dimensional integrable systems Lax representation r-matrix algebras separation of variables 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. V. Sokolov
    • 1
  • A. V. Tsiganov
    • 2
  1. 1.Landau Institute of Theoretical PhysicsMoscowRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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