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arXiv · 2404.02055

On Hamiltonian Structures of Partial Difference Equations

Zhonglun Cao
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Abstract

We first introduce the notion of Hamiltonian structure for a partial difference equation. Then we construct some infinite quivers, and realize the discrete KdV equation, the Hirota-Miwa equation and its various reductions as the mutation relations of the corresponding cluster algebras. Finally, we show that the log-canonical Poisson structures associated to these cluster algebras give the Hamiltonian structures or the bihamiltonian structures of these partial difference equations.

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Zhonglun Cao. 2024-04-02. On Hamiltonian Structures of Partial Difference Equations. https://arxiv.org/abs/2404.02055

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