中国物理B ›› 2008, Vol. 17 ›› Issue (5): 1574-1580.doi: 10.1088/1674-1056/17/5/007

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The multicomponent (2+1)-dimensional Glachette--Johnson (GJ) equation hierarchy and its super-integrable coupling system

张鸿庆1, 于发军2   

  1. (1)Department of Mathematics, Dalian University of Technology, Dalian 116024, China; (2)School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China;Department of Mathematics, Dalian University of Technology, Dalian 116024, China
  • 收稿日期:2007-07-23 修回日期:2007-08-25 出版日期:2008-05-20 发布日期:2008-05-20
  • 基金资助:
    Project supported by the National Key Basic Research Development of China (Grant No 2004CB318000).

The multicomponent (2+1)-dimensional Glachette--Johnson (GJ) equation hierarchy and its super-integrable coupling system

Yu Fa-Jun(于发军)a)b)† and Zhang Hong-Qing(张鸿庆)b)   

  1. a School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China; b Department of Mathematics, Dalian University of Technology, Dalian 116024, China
  • Received:2007-07-23 Revised:2007-08-25 Online:2008-05-20 Published:2008-05-20
  • Supported by:
    Project supported by the National Key Basic Research Development of China (Grant No 2004CB318000).

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摘要： This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra \tilde{A}M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette--Johnson (GJ) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem.

关键词: matrix Lie algebra, multicomponent GJ hierarchy, super-integrable coupling system

Abstract: This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra $\tilde{A}_M$. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette--Johnson (GJ) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem.

Key words: matrix Lie algebra, multicomponent GJ hierarchy, super-integrable coupling system

中图分类号:  (Solitons)

  • 05.45.Yv
02.10.Ud (Linear algebra) 02.10.Yn (Matrix theory) 02.30.Ik (Integrable systems)