Semi-direct sums of Lie algebras and continuous integrable couplings |
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Institution: | 1. Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA;2. College of Science, Shandong University of Science and Technology, Qingdao 266510, PR China;3. School of Mathematics, Liaoning Normal University, Dalian 116029, PR China |
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Abstract: | A relation between semi-direct sums of Lie algebras and integrable couplings of continuous soliton equations is presented, and correspondingly, a feasible way to construct integrable couplings is furnished. A direct application to the AKNS spectral problem leads to a novel hierarchy of integrable couplings of the AKNS hierarchy of soliton equations. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards complete classification of integrable systems. |
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