中国物理B ›› 2007, Vol. 16 ›› Issue (3): 595-598.doi: 10.1088/1009-1963/16/3/006

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The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure

杨耕文1, 许曰才2, 岳超3   

  1. (1)Editorial Department of Journal of Luoyang University,Luoyang 471023, China; (2)School of Adult Education, Shandong University of Science and Technology, Taian 271000, China; (3)School of Information Engineering, Taishan Medical University, Taian 271016, China
  • 收稿日期:2006-06-24 修回日期:2006-07-06 出版日期:2007-03-20 发布日期:2007-03-20

The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure

Yue Chao(岳超)a)†, Yang Geng-Wen(杨耕文)b), and Xu Yue-Cai(许曰才)c)   

  1. a School of Information Engineering, Taishan Medical University, Taian 271016, China; b Editorial Department of Journal of Luoyang University, Luoyang 471023, China; c School of Adult Education, Shandong University of Science and Technology, Taian 271000, China
  • Received:2006-06-24 Revised:2006-07-06 Online:2007-03-20 Published:2007-03-20

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摘要： In this paper a type of 9-dimensional vector loop algebra \tilde{F} is constructed, which is devoted to establish an isospectral problem. It follows that a Liouville integrable coupling system of the m-AKNS hierarchy is obtained by employing the Tu scheme, whose Hamiltonian structure is worked out by making use of constructed quadratic identity. The method given in the paper can be used to obtain many other integrable couplings and their Hamiltonian structures.

关键词: loop algebra, integrable coupling, Hamiltonian structure, quadratic identity

Abstract: In this paper a type of 9-dimensional vector loop algebra $\tilde{F}$ is constructed, which is devoted to establish an isospectral problem. It follows that a Liouville integrable coupling system of the m-AKNS hierarchy is obtained by employing the Tu scheme, whose Hamiltonian structure is worked out by making use of constructed quadratic identity. The method given in the paper can be used to obtain many other integrable couplings and their Hamiltonian structures.

Key words: loop algebra, integrable coupling, Hamiltonian structure, quadratic identity

中图分类号:  (Integrable systems)

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