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Integrable decomposition of a hierarchy of soliton equations and integrable coupling system by semidirect sums of Lie algebras
Authors:Lin Luo  Engui Fan
Institution:1. Department of Mathematics, Xiaogan University, Xiaogan 432100, Hubei, China;2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China
Abstract:Staring from a new spectral problem, a hierarchy of the soliton equations is derived. It is shown that the associated hierarchies are infinite-dimensional integrable Hamiltonian systems. By the procedure of nonlinearization of the Lax pairs, the integrable decomposition of the whole soliton hierarchy is given. Further, we construct two integrable coupling systems for the hierarchy by the conception of semidirect sums of Lie algebras.
Keywords:02  30  Ik
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