Matrix semidiscrete Ablowitz-Ladik equation hierarchy and a matrix discrete second Painlevé equation
Matrix semidiscrete Ablowitz-Ladik equation hierarchy and a matrix discrete second Painlevé equation
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DOI：
10.1063/1.3397483
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发表时间：
2010-05
影响因子：
1.3
通讯作者：
P. R. Gordoa;A. Pickering;Zuo-nong Zhu
中科院分区：
文献类型：
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作者：
P. R. Gordoa;A. Pickering;Zuo-nong Zhu
在本文中，我们首先证明，通过考虑矩阵半离散 Ablowitz-Ladik 等谱线性问题，半离散 Ablowitz-Ladik 方程层次可以扩展到矩阵情况。然后我们将这个线性问题扩展到非等谱情况，并构造一个新的耦合矩阵半离散可积方程。结果表明，该新矩阵半离散可积方程的连续统极限是耦合矩阵变系数修正的Korteweg-de Vries方程，并且可以得到矩阵离散第二Painleve方程作为该新矩阵半离散方程的平稳约简。
In this article, we first show that the semidiscrete Ablowitz–Ladik equation hierarchy can be extended to the matrix case by considering a matrix semidiscrete Ablowitz–Ladik isospectral linear problem. We then extend this linear problem to the nonisospectral case, and a new coupled matrix semidiscrete integrable equation is constructed. It is shown that the continuum limit of this new matrix semidiscrete integrable equation is the coupled matrix variable-coefficient modified Korteweg-de Vries equation and that a matrix discrete second Painleve equation can be obtained as a stationary reduction in this new matrix semidiscrete equation.