On the bi-Hamiltonian structure of Toda and relativistic Toda lattices

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Abstract

We introduce a general quadratic Poisson bracket on the associative algebra equipped with non-degenerate scalar product. With the help of this bracket we obtain the interpretation of the Toda and relativistic Toda lattices as the restrictions of one and the same bi-Hamiltonian system to two different low-dimensional manifolds, which are Poisson submanifolds with respect to two brackets simultaneously.

Original languageEnglish
Pages (from-to)419-429
Number of pages11
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume180
Issue number6
DOIs
StatePublished - 20 Sep 1993
Externally publishedYes

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