Bogoyavlensky--Volterra and Birkhoff Integrable Systems

Details Bogoyavlensky--Volterra and Birkhoff Integrable Systems Bogoyavlensky--Volterra and Birkhoff Integrable Systems

2006-08-21

arxiv.org/abs/math-ph/0608051v1

Physica D, 195, 50-60 (2004)

Physics

Mathematical Physics

21 pages

Scientific paper

10.1016/j.physd.2004.03.009

In this paper we examine an interesting connection between the generalized Volterra lattices of Bogoyavlensky and a special case of an integrable system defined by Sklyanin. The Sklyanin system happens to be one of the cases in the classification of Kozlov and Treshchev of Birkhoff integrable Hamiltonian systems. Using this connection we demonstrate the integrability of the system and define a new Lax pair representation. In addition, we comment on the bi--Hamiltonian structure of the system.

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