Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach
Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach
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DOI：
10.1111/sapm.12007
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发表时间：
2012-08
影响因子：
2.7
通讯作者：
D.‐J. Zhang;S. Zhao
中科院分区：
文献类型：
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作者：
D.‐J. Zhang;S. Zhao
通常的柯西矩阵方法从已知的平波因子向量r和已知的修饰柯西矩阵M开始。本文从一个r和M待定的确定矩阵方程组出发。从确定方程组中，我们可以建立一些定义的标量函数的移位关系，然后导出格方程。确定方程组允许r和M有更多的选择，本文给出了所有可能的r和M的显式表达式。作为应用，我们得到了许多格点方程的多孤子解，包括格点势KdV方程、格点势修正KdV方程、格点Schwarzian KdV方程、NQC方程以及ABS列表中的一些格点方程。
The usual Cauchy matrix approach starts from a known plain wave factor vector r and known dressed Cauchy matrix M . In this paper, we start from a determining matrix equation set with undetermined r and M . From the determining equation set we can build shift relations for some defined scalar functions and then derive lattice equations. The determining equation set admits more choices for r and M and in the paper we give explicit formulae for all possible r and M . As applications, we get more solutions than usual multisoliton solutions for many lattice equations including the lattice potential KdV equation, the lattice potential modified KdV equation, the lattice Schwarzian KdV equation, NQC equation, and some lattice equations in ABS list.