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Zbl 1234.37049
Ma, Wen-Xiu; Xu, Xixiang; Zhang, Yufeng
Semi-direct sums of Lie algebras and continuous integrable couplings. (English)
[J] Phys. Lett., A 351, No. 3, 125-130 (2006). ISSN 0375-9601

Summary: 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.

MSC 2000:: *37K30 Relations with algebraic structures
17B80 Applications of Lie algebras to integrable systems

Keywords: semi-direct sums of Lie algebras; zero curvature equations; integrable couplings; symmetries

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Zentralblatt MATH Berlin [Germany]