中国物理B ›› 2004, Vol. 13 ›› Issue (2): 132-138.doi: 10.1088/1009-1963/13/2/002

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A subalgebra of loop algebra ?2 and its applications

谭汉华1, 张玉峰2, 郭福奎2   

  1. (1)Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China; (2)Institute of Mathematics, Information School, Shandong University of Science and Technology, Taian 271019, China
  • 收稿日期:2003-05-30 修回日期:2003-08-28 出版日期:2004-02-06 发布日期:2005-07-06

A subalgebra of loop algebra $\tilde{A}_2$ and its applications

Zhang Yu-Feng (张玉峰)a, Tam Hon-Wah (谭汉华)b, Guo Fu-Kui (郭福奎)a   

  1. a Institute of Mathematics, Information School, Shandong University of Science and Technology, Taian 271019, China; b Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
  • Received:2003-05-30 Revised:2003-08-28 Online:2004-02-06 Published:2005-07-06

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摘要： A subalgebra of loop algebra ?_2 and its expanding loop algebra \overline{G} are constructed. It follows that both resulting integrable Hamiltonian hierarchies are obtained. As a reduction case of the first hierarchy, a generalized nonlinear coupled Schr?dinger equation, the standard heat-conduction and a formalism of the well known Ablowitz, Kaup, Newell and Segur hierarchy are given, respectively. As a reduction case of the second hierarchy, the nonlinear Schr?dinger and modified Korteweg de Vries hierarchy and a new integrable system are presented. Especially, a coupled generalized Burgers equation is generated.

关键词: loop algebra, integrable hierarchy, Hamiltonian structure

Abstract: A subalgebra of loop algebra $\tilde{A}_2$ and its expanding loop algebra $\overline{G}$ are constructed. It follows that both resulting integrable Hamiltonian hierarchies are obtained. As a reduction case of the first hierarchy, a generalized nonlinear coupled Schr?dinger equation, the standard heat-conduction and a formalism of the well known Ablowitz, Kaup, Newell and Segur hierarchy are given, respectively. As a reduction case of the second hierarchy, the nonlinear Schr?dinger and modified Korteweg de Vries hierarchy and a new integrable system are presented. Especially, a coupled generalized Burgers equation is generated.

Key words: loop algebra, integrable hierarchy, Hamiltonian structure

中图分类号:  (Logic, set theory, and algebra)

  • 02.10.-v
03.65.Ge (Solutions of wave equations: bound states) 44.10.+i (Heat conduction) 02.30.Hq (Ordinary differential equations) 02.30.Rz (Integral equations)