论文标题
与晶格KDV方程相关的离散hirota降低
Discrete Hirota reductions associated with the lattice KdV equation
论文作者
论文摘要
我们研究了作为离散海洛塔方程的减少，获得的一组生物图，这与晶格KDV方程的行进波解决方案有关。特别是，对于与晶格上有理性速度N/m移动的波的减少，n，m是副整体，我们证明了当n + m奇数时，地图的liouville集成性，并且证明了一般情况的各种特性。我们的构建有两种主要成分：与每个hirota双线性方程相关的群集代数，它们提供了不变的（前）符号和泊松结构；以及敷料链的单层矩阵与KDV行驶波减少的连接。
We study the integrability of a family of birational maps obtained as reductions of the discrete Hirota equation, which are related to travelling wave solutions of the lattice KdV equation. In particular, for reductions corresponding to waves moving with rational speed N/M on the lattice, where N,M are coprime integers, we prove the Liouville integrability of the maps when N + M is odd, and prove various properties of the general case. There are two main ingredients to our construction: the cluster algebra associated with each of the Hirota bilinear equations, which provides invariant (pre)symplectic and Poisson structures; and the connection of the monodromy matrices of the dressing chain with those of the KdV travelling wave reductions.
