Lie Algebras for Constructing Nonlinear Integrable and Bi-Integrable Hamiltonian Couplings
Received:March 24, 2014  Revised:January 16, 2015
Key Words: Lie algebra   integrable couplings   bi-integrable couplings   Hamiltonian structure  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.61273011; 11401392).
Author NameAffiliation
Xiaohong CHEN Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China
School of Science, University of Science and Technology Liaoning, Liaoning 114051, P. R. China 
Hongqing ZHANG Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China 
Fucai YOU Department of Basic Sciences, Shenyang Institute of Engineering, Liaoning 110136, P. R. China 
Daqing ZHANG School of Science, University of Science and Technology Liaoning, Liaoning 114051, P. R. China 
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Abstract:
      With the help of a Lie algebra, two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings. For illustrating the application of the Lie algebras, an integrable Hamiltonian system is obtained, from which some reduced evolution equations are presented. Finally, Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity. The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system.
Citation:
DOI:10.3770/j.issn:2095-2651.2015.03.007
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