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̵ļsԓeõKNCLLGILaxHamiltonYĽyһ@ʽʽ Integrable systems of derivative nonlinear Schr odinger type and their multiHamiltonian structure Engui
Fan Institute of Mathematics, Fudan University, Shanghai 200433, PR China Received 1 September 2000, in final form 6 December 2000 Abstract:A spectral problem and the associated hierarchy of Schr odinger type equations are proposed. It is shown that the hierarchy is integrable in Liouvilles sense and possesses multiHamiltonian structure. It is found that several kinds of important equation such as the KaupCNewell (KN) equation, the ChenCLeeCLiu (CLL) equation, the GerdjikovCIvanov (GI) equation, the modified KortewegCde Vries equation and the SharmaCTassoCOlever equation are members in the hierarchy as its special reductions. Moreover, KN, CLL and GI equations are described by using a unified generalized derivative Schr odinger equation involving a parameter, and their Hamiltonian structure and Lax pairs are also given by unified and explicit formulae. 1g[ȫҪʹܛAbode Acrobat(ܛ^Ҋ,վṩd) 2dՓȫՈc(64KB) վ䛵ıߵՓģ 1The zero curvature representation for hierarchies of nonlinear evolution equations 2Extended tanhfunction method and its applications to nonlinear equations 3Soliton solutions for a generalized HirotaCSatsuma coupled KdV equation and a coupled MKdV equation 5Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method

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