Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models |
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| Authors: | V. V. Sokolov A. V. Tsiganov |
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| Affiliation: | (1) Landau Institute of Theoretical Physics, Moscow, Russia;(2) St. Petersburg State University, St. Petersburg, Russia |
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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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| Keywords: | finite-dimensional integrable systems Lax representation r-matrix algebras separation of variables |
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