On Hamiltonian Structures of Partial Difference Equations
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916189575315456 |
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| author | Cao, Zhonglun |
| author_facet | Cao, Zhonglun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hamiltonian Structures of Partial Difference Equations Cao, Zhonglun Mathematical Physics 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. |
| title | On Hamiltonian Structures of Partial Difference Equations |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2404.02055 |