中国物理B ›› 2007, Vol. 16 ›› Issue (3): 605-610.doi: 10.1088/1009-1963/16/3/008

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Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

尤福财1, 夏铁成2   

  1. (1)Department of Mathematics, Shanghai University, Shanghai 200444, China; (2)Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Mathematics, Tianjin University, Tianjin 300072, China
  • 收稿日期:2006-04-13 修回日期:2006-09-12 出版日期:2007-03-20 发布日期:2007-03-20
  • 基金资助:
    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).

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

Xia Tie-Cheng(夏铁成)a)b)† and You Fu-Cai(尤福财)a)   

  1. a Department of Mathematics, Shanghai University, Shanghai 200444, China; b Department of Mathematics, Tianjin University, Tianjin 300072, China
  • Received:2006-04-13 Revised:2006-09-12 Online:2007-03-20 Published:2007-03-20
  • Supported by:
    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).

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摘要： 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.

关键词: loop algebra, zero curvature equation, multi-component Dirac equation hierarchy, multi-component integrable couplings system

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.

Key words: loop algebra, zero curvature equation, multi-component Dirac equation hierarchy, multi-component integrable couplings system

中图分类号:  (Algebraic methods)

  • 03.65.Fd
02.10.Ud (Linear algebra) 02.30.Ik (Integrable systems) 03.65.Ge (Solutions of wave equations: bound states) 05.45.Yv (Solitons)