| Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System |
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| 作者姓名： | XIA Tie-Cheng YOU Fu-Cai |
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| 作者单位： | Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| 基金项目： | The project supported by National Natural Science Foundation of China under Grant No. 10371070, the Science Foundation of Liuhui Center of Tianjin University and Nankai University, and the Science Foundation of Educational Committee of Liaoning Province of China under Grant No. 2004C057 |
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| 摘 要： |
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| 关 键 词： | Lie代数 可积分耦合函数 环代数 TC层次 |
| 收稿时间： | 2004-12-07 |
| 修稿时间： | 2004-12-072005-02-18 |
Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System |
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| XIA Tie-Cheng YOU Fu-Cai.Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System[J].Communications in Theoretical Physics,2005,44(5):793-798. |
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| Authors: | XIA;Tie-Cheng;YOU;Fu-Cai |
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| Abstract: | A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding 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 multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC 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 generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach. |
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| Keywords: | loop algebra multi-component TC hierarchy multi-component integrable coupling system |
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