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arXiv · 1806.07233

Poisson structures for difference equations

Charalampos A. Evripidou·G. R. W. Quispel·John A. G. Roberts
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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.

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Charalampos A. Evripidou, G. R. W. Quispel, John A. G. Roberts. 2018-06-19. Poisson structures for difference equations. https://doi.org/10.1088/1751-8121/aae746

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