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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 3, Pages 191–203
DOI: https://doi.org/10.1134/S1560354708030052 (Mi rcd570) 		 
This article is cited in 12 scientific papers (total in 12 papers)

The Poisson Bracket Compatible with the Classical Reflection Equation Algebra

A. V. Tsiganov

V. A. Fock Institute of Physics, St. Petersburg State University, Petrodvorets, ul. Ulyanovskaya 1, St. Petersburg, 198504 Russia
Citations (12)
DOI: https://doi.org/10.1134/S1560354708030052
Abstract: We introduce a family of compatible Poisson brackets on the space of $2 \times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes the $XXX$ Heisenberg magnet with boundary conditions, the generalized Toda lattices and the Kowalevski top.
Keywords: Poisson bracket, bi-hamiltonian structure, reflection equation algebra.
Received: 07.09.2007
Accepted: 08.05.2008
Bibliographic databases:
Document Type: Article
MSC: 70H20, 70H06, 37K10
Language: English
Citation: A. V. Tsiganov, “The Poisson Bracket Compatible with the Classical Reflection Equation Algebra”, Regul. Chaotic Dyn., 13:3 (2008), 191–203
Citation in format AMSBIB
\Bibitem{Tsi08}
\by A.~V.~Tsiganov
\paper The Poisson Bracket Compatible with the Classical Reflection Equation Algebra
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 3
\pages 191--203
\mathnet{http://mi.mathnet.ru/rcd570}
\crossref{https://doi.org/10.1134/S1560354708030052}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2415373}
\zmath{https://zbmath.org/?q=an:1229.70061}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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