Bogoyavlensky-Volterra and Birkhoff integrable systems
Date
2004Source
Physica D: Nonlinear PhenomenaVolume
195Issue
1-2Pages
50-66Google Scholar check
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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. © 2004 Elsevier B.V. All rights reserved.