2024/04/02 by Zhonglun Cao, Cao, Zhonglun
Mathematics · #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2404.02055
openalex publication_date 2024/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.