Compatible Poisson Structures of Toda Type Discrete Hierarchy
Exactly Solvable and Integrable Systems
2009-11-10 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.nlin/0402014,
title = {Compatible Poisson Structures of Toda Type Discrete Hierarchy},
author = {H. Aratyn and K. Bering},
journal= {arXiv preprint arXiv:nlin/0402014},
year = {2009}
}
Comments
22 pages, LaTeX, v3: Minor changes