Publication details

Compatible Poisson Structures of Toda Type Discrete Hierarchy

Authors

ARATYN Henrik BERING LARSEN Klaus

Year of publication 2004
Type Article in Periodical
Magazine / Source INTERNATIONAL JOURNAL OF MODERN PHYSICS A
MU Faculty or unit

Faculty of Science

Citation
Web http://arxiv.org/abs/nlin/0402014
Doi http://dx.doi.org/10.1142/S0217751X05021087
Field Theoretical physics
Keywords Integrable Systems; Classical R-Matrix; Discrete Toda Lattice; Compatible Poisson Brackets
Description 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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