Abstract A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra $\tilde{X}$ is produced. By taking advantage of $\tilde{X}$, 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 $\tilde{F}$M of the loop algebra $\tilde{X}$ is presented. Based on the $\tilde{F}$M, 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.
Received: 13 April 2006
Revised: 12 September 2006
Accepted manuscript online:
Fund: Project supported by the Liuhui Applied
Mathematics Center of Nankai University and Tianjin
University, China (Grant No T34), Educational Committee of Liaoning
Province, China (Grant No 2004C057) and Science Funds of Shanghai
Education Committee, China (Grant No~06AZ081).
Cite this article:
Xia Tie-Cheng(夏铁成) and You Fu-Cai(尤福财) Multi-component Dirac equation hierarchy and its multi-component integrable couplings system 2007 Chinese Physics 16 605
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