Compatible Poisson Structures of Toda Type Discrete Hierarchy

Details Compatible Poisson Structures of Toda Type Discrete Hierarchy Compatible Poisson Structures of Toda Type Discrete Hierarchy

2004-02-11

arxiv.org/abs/nlin/0402014v3

Int.J.Mod.Phys. A20 (2005) 1367-1388

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, LaTeX, v3: Minor changes

Scientific paper

10.1142/S0217751X05021087

An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and non-local families of R-matrix solutions to the modified Yang-Baxter equation. The three R-theoretic Poisson structures and the Suris quadratic bracket are derived. The resulting family of bi-Poisson structures include a seminal discrete bi-Poisson structure of Kupershmidt at a special value.

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