Two expanding forms of a Lie algebra and their application

doi:10.1088/1009-1963/12/6/301

中国物理B ›› 2003, Vol. 12 ›› Issue (6): 581-585.doi: 10.1088/1009-1963/12/6/301

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Two expanding forms of a Lie algebra and their application

魏小鹏¹, 闫庆友², 张玉峰³

(1)Centre of Advanced Design Technology, Dalian University, Dalian 116622, China; (2)Centre of Advanced Design Technology, Dalian University, Dalian 116622, China; School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China; (3)Institute of Computation Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China; School of Information Science and Engineering, Shandong University of Science and Technology, Taian 271019, China

收稿日期:2002-12-27 修回日期:2002-09-28 出版日期:2003-06-16 发布日期:2005-03-16
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos 50275013 and G60174037).

Two expanding forms of a Lie algebra and their application

Yan Qing-You (闫庆友)^ab, Zhang Yu-Feng (张玉峰)^cd, Wei Xiao-Peng (魏小鹏)^a

^a Centre of Advanced Design Technology, Dalian University, Dalian 116622, China; ^b School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China; ^c Institute of Computation Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China^d School of Information Science and Engineering, Shandong University of Science and Technology, Taian 271019, China

Received:2002-12-27 Revised:2002-09-28 Online:2003-06-16 Published:2005-03-16
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos 50275013 and G60174037).

摘要/Abstract

摘要： With the help of a known Lie algebra, two new high order Lie algebras are constructed. It is remarkable that they have different constructing approaches. The first Lie algebra is constructed by the definition of integrable couplings, the second one by an extension of Lie algebra. Then by making use of Tu scheme, a generalized AKNS hierarchy and another new hierarchy are obtained. As a reduction case of the first hierarchy, a kind of coupled KdV equation is presented. As a reduction case of the second one, a new coupled Schr?dinger equation is given.

Abstract: With the help of a known Lie algebra, two new high order Lie algebras are constructed. It is remarkable that they have different constructing approaches. The first Lie algebra is constructed by the definition of integrable couplings, the second one by an extension of Lie algebra. Then by making use of Tu scheme, a generalized AKNS hierarchy and another new hierarchy are obtained. As a reduction case of the first hierarchy, a kind of coupled KdV equation is presented. As a reduction case of the second one, a new coupled Schr?dinger equation is given.

Key words: loop algebra, integrable coupling, Tu scheme, AKNS hierarchy

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

02.30.Hq (Ordinary differential equations) 03.65.Ge (Solutions of wave equations: bound states) 02.30.Ik (Integrable systems) 05.45.Yv (Solitons)

闫庆友, 张玉峰, 魏小鹏. Two expanding forms of a Lie algebra and their application[J]. 中国物理B, 2003, 12(6): 581-585.

Yan Qing-You (闫庆友), Zhang Yu-Feng (张玉峰), Wei Xiao-Peng (魏小鹏). Two expanding forms of a Lie algebra and their application[J]. Chinese Physics, 2003, 12(6): 581-585.

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Two expanding forms of a Lie algebra and their application

Two expanding forms of a Lie algebra and their application

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