Multi-component Dirac equation hierarchy and its multi-component integrable couplings system |
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Authors: | Xia Tie-Cheng and You Fu-Cai |
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Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, China; Department of Mathematics, Tianjin University, Tianjin 300072, China |
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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. |
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Keywords: | loop algebra zero curvature equation multi-component Dirac equation hierarchy multi-component integrable couplings system |
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