中国物理B ›› 2007, Vol. 16 ›› Issue (3): 588-594.doi: 10.1088/1009-1963/16/3/005

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Two types of loop algebras and their expanding Lax integrable models

岳超1, 张玉峰2, 魏媛2   

  1. (1)School of Information Engineering, Taishan Medical University, Taian 271016, China; (2)School of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
  • 收稿日期:2005-06-10 修回日期:2006-04-14 出版日期:2007-03-20 发布日期:2007-03-20

Two types of loop algebras and their expanding Lax integrable models

Yue Chao(岳超)a)†, Zhang Yu-Feng(张玉峰)b)‡, and Wei Yuan(魏媛)b)   

  1. a School of Information Engineering, Taishan Medical University, Taian 271016, China; b School of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
  • Received:2005-06-10 Revised:2006-04-14 Online:2007-03-20 Published:2007-03-20

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摘要： Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation Ut-Vx+[U,V]=0, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator \widetilde{J} is presented by constructing a subalgebra \widetilde{G } of the loop algebra \widetilde A2. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.

关键词: zero-curvature equation, integrable hierarchy, loop algebra

Abstract: Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation $U _{t}-V_  {x}+[U,V]=0$, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator $\widetilde{J}$ is presented by constructing a subalgebra $\widetilde{G}$ of the loop algebra $\widetilde{A}_{2}$. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.

Key words: zero-curvature equation, integrable hierarchy, loop algebra

中图分类号:  (Integrable systems)

  • 02.30.Ik
02.10.Ud (Linear algebra) 05.45.Yv (Solitons)