论文标题
与离散的korteweg-de vries-type方程相关的可集成的符号图
Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations
论文作者
论文摘要
在本文中，我们介绍了与普通差异方程式相关的新型可整合符号图，并显示它们如何以非常多样化的方式确定可集成的部分差异方程，包括可松弛和显式解决方案，这些方程是Korteweg-de vries-de vries-typepepe（Kdepe）的可离散的部分差分方程。因此，证明了几种不同的汉密尔顿系统通过liouville集成性框架导致一个和相同的差异方程式。因此，这些可整合的符号图可以为表征和确定部分差异方程的集成性提供有效的工具。
In this paper we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable partial difference equations which are the discrete counterparts of integrable partial differential equations of Korteweg-de Vries-type (KdV-type). As a consequence it is demonstrated that several distinct Hamiltonian systems lead to one and the same difference equation by means of the Liouville integrability framework. Thus, these integrable symplectic maps may provide an efficient tool for characterizing, and determining the integrability of, partial difference equations.
