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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 3, Pages 485–500
DOI: https://doi.org/10.4213/tmf413 (Mi tmf413) 		 
This article is cited in 15 scientific papers (total in 15 papers)

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

V. V. Sokolova, A. V. Tsiganovb

a Landau Institute for Theoretical Physics, Centre for Non-linear Studies
b St. Petersburg State University, Faculty of Physics
Full-text PDF (274 kB) Citations (15)
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DOI: https://doi.org/10.4213/tmf413
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.
Keywords: finite-dimensional integrable systems, Lax representation, $r$-matrix algebras, separation of variables.
English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 3, Pages 1730–1743
DOI: https://doi.org/10.1023/A:1021326727968
Bibliographic databases:
Language: Russian
Citation: V. V. Sokolov, A. V. Tsiganov, “Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models”, TMF, 133:3 (2002), 485–500; Theoret. and Math. Phys., 133:3 (2002), 1730–1743
Citation in format AMSBIB
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\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 3
\pages 1730--1743
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  • https://www.mathnet.ru/eng/tmf/v133/i3/p485
    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:66
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