Multi-component Dirac equation hierarchy and its multi-component integrable couplings system
Multi-component Dirac equation hierarchy and its multi-component integrable couplings system
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DOI：
10.1088/1009-1963/16/3/008
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
Tie-Cheng Xia;Fu-Cai You
中科院分区：
文献类型：
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作者：
Tie-Cheng Xia;Fu-Cai You
提出了一种生成多分量可积方程族的通用方案。给出了一个简单的3M维循环代数X̃。利用X-̃建立了一个新的等谱问题，然后利用屠格式得到了多分量狄拉克方程组。最后，给出了循环代数X̃的扩展循环代数F̃M。基于F-̃M，研究了多分量狄拉克方程族的多分量可积耦合系统。该方法也适用于其他非线性发展方程组。
A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra X̃ is produced. By taking advantage of X̃, a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra F̃M of the loop algebra X̃ is presented. Based on the F̃M, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.