论文标题
晶格KDV方程和与ABS晶格方程的连接的本征函数方程
Eigenfunction equations of lattice KdV equations and connections to ABS lattice equations with a $δ$ term
论文作者
论文摘要
我们开发了晶格KDV方程的晶格特征功能方程，这些方程是由晶状体KDV方程的LAX对遵守的方程式或特征函数所遵循的。这导致三维一致的四边形方程与Adler-Bobenko-Suris（ABS）分类中的晶格方程密切相关。特别是，我们展示了ABS列表中的H3（$δ$），Q1（$δ$）和Q3（$δ$）方程是如何通过对$δ$项的自然解释作为特征函数之间的相互作用来提供的。通过构造，获得了这些方程的精确溶液结构。本文介绍的方法可以用作搜索可集成晶格方程的系统手段。
We develop lattice eigenfunction equations of lattice KdV equation, which are equations obeyed by the auxiliary functions, or eigenfunctions, of the Lax pair of the lattice KdV equation. This leads to three-dimensionally consistent quad-equations that are closely related to lattice equations in the Adler-Bobenko-Suris (ABS) classification. In particular, we show how the H3($δ$), Q1($δ$) and Q3($δ$) equations in the ABS list arise from the lattice eigenfunction equations by providing a natural interpretation of the $δ$ term as interactions between the eigenfunctions. By construction, exact solution structures of these equations are obtained. The approach presented in this paper can be used as a systematic means to search for integrable lattice equations.
