A family of new integrable couplings with two arbitrary functions of TC hierarchy
A family of new integrable couplings with two arbitrary functions of TC hierarchy
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DOI：
10.1063/1.1501165
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发表时间：
2002-09
影响因子：
1.3
通讯作者：
Zhenya Yan;Hong-qing Zhang
中科院分区：
文献类型：
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作者：
Zhenya Yan;Hong-qing Zhang
寻找已知演化方程的可积层次的新的可积耦合是一个非常有趣的新方面，在孤子理论中具有重要意义。本文首先给出了一个环代数P及其基。其次，考虑了环代数P中具有四个势的新的等谱问题，利用零曲率方程构造了已知的TC层次的可积耦合，从而得到了包含两个任意函数的新的可积耦合族。特别地，当我们令两个任意函数为零时，还给出了广义Korteweg-de Vries方程的一种特殊的可积耦合。
Seeking new integrable couplings of the known integrable hierarchies of evolution equations is a quite new interesting aspect and is of great significance in soliton theory. In this paper, a loop algebra P and its basis are first presented. Second, a new isospectral problem with four potentials in the loop algebra P is considered to construct integrable couplings of the well-known TC hierarchy by the zero-curvature equation such that a family of new integrable couplings including two arbitrary functions are obtained. In particular, when we set two arbitrary functions to be zero, a special integrable couplings of the generalized Korteweg–de Vries equation is also given.