Multi-component Levi Hierarchy and Its Multi-component Integrable Coupling System |
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Authors: | XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying |
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Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, China Department of Mathematics, Shanghai University, Shanghai 200444, China Department of Mathematics, Bohai University, Jinzhou 121000, China |
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Abstract: | A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multicomponent integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies. |
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Keywords: | loop algebra multi-component Levi hierarchy multi-component integrable coupling system |
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