English

Poisson structures for difference equations

Exactly Solvable and Integrable Systems 2018-11-02 v2

Abstract

We study the existence of log-canonical Poisson structures that are preserved by difference equations of special form. We also study the inverse problem, given a log-canonical Poisson structure to find a difference equation preserving this structure. We give examples of quadratic Poisson structures that arise for the Kadomtsev-Petviashvili (KP) type maps which follow from a travelling-wave reduction of the corresponding integrable partial difference equation.

Keywords

Cite

@article{arxiv.1806.07233,
  title  = {Poisson structures for difference equations},
  author = {Charalampos A. Evripidou and G. R. W. Quispel and John A. G. Roberts},
  journal= {arXiv preprint arXiv:1806.07233},
  year   = {2018}
}

Comments

20 pages, 27 references