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, Chinad School of Information Science and Engineering, Shandong University of Science and Technology, Taian 271019, China
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.
Received: 27 December 2002
Revised: 28 September 2002
Accepted manuscript online:
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