中国物理B ›› 2005, Vol. 14 ›› Issue (2): 247-250.doi: 10.1088/1009-1963/14/2/005

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The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system

张玉峰1, 夏铁成2, 汪宏3   

  1. (1)Department of Mathematics, Liaoning Normal University, Dalian 116022, China; (2)Department of Mathematics, Tianjin University, Tianjin 300072, China; Department of Mathematics, Bohai University, Jinzhou 121000, China; (3)Department of Physics, Tianjin University, Tianjin 300072, China
  • 收稿日期:2003-10-08 修回日期:2004-09-27 出版日期:2005-03-02 发布日期:2005-03-02
  • 基金资助:
    Projet supported by the National Natural Science Foundation of China (Grant No 10371070), the Special Funds for Major Specialities of Shanghai Educational Committee and Natural Science Foundation of Educational Committee of Liaoning Province.

The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system

Xia Tie-Cheng (夏铁成)ab, Wang Hong (汪宏)c, Zhang Yu-Feng (张玉峰)d   

  1. a Department of Mathematics, Tianjin University, Tianjin 300072, China; b Department of Mathematics, Bohai University, Jinzhou 121000, China; c Department of Physics, Tianjin University, Tianjin 300072, Chinad  Department of Mathematics, Liaoning Normal University, Dalian 116022, China
  • Received:2003-10-08 Revised:2004-09-27 Online:2005-03-02 Published:2005-03-02
  • Supported by:
    Projet supported by the National Natural Science Foundation of China (Grant No 10371070), the Special Funds for Major Specialities of Shanghai Educational Committee and Natural Science Foundation of Educational Committee of Liaoning Province.

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摘要： A new simple loop algebra \widetilde{G}M is constructed, which is devoted to the establishing of an isospectral problem. By making use of the Tu scheme, the multi-component Tu hierarchy is obtained. Furthermore, an expanding loop algebra \widetilde{F}M of the loop algebra \widetilde{G}M is presented. Based on the \widetilde{F}M, the multi-component integrable coupling system of the multi-component Tu hierarchy has been worked out. The method can be applied to other nonlinear evolution equation hierarchies.

关键词: loop algebra, Tu hierarchy, integrable couplings system

Abstract: A new simple loop algebra $\widetilde{G}_M$ is constructed, which is devoted to the establishing of an isospectral problem. By making use of the Tu scheme, the multi-component Tu hierarchy is obtained. Furthermore, an expanding loop algebra $\widetilde{F}_M$ of the loop algebra $\widetilde{G}_M$ is presented. Based on the $\widetilde{F}_M$, the multi-component integrable coupling system of the multi-component Tu hierarchy has been worked out. The method can be applied to other nonlinear evolution equation hierarchies.

Key words: loop algebra, Tu hierarchy, integrable couplings system

中图分类号:  (Solitons)

  • 05.45.Yv
02.10.Ud (Linear algebra) 02.10.Yn (Matrix theory)