导数Schrodinger型方程族及其多Hamilton结构 范恩贵 摘要:本文提出一个谱问题并由此导出一导数Schrodinger型方程族,证明了该方程族在Liouville意义下可积并拥有多Hamilton结构,发现几类著名的方程,如KN、CLL、GI、STO
方程等,均可做为特殊的约化包含在该方程族中,特别得到了KN、CLL、GI方程Lax对、Hamilton结构的统一、显式公式。 Integrable systems of derivative nonlinear Schr¨ odinger type and their multi-Hamiltonian 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 Liouville’s sense and possesses multi-Hamiltonian structure. It is found that several kinds of important equation such as the Kaup–Newell (KN) equation, the Chen–Lee–Liu (CLL) equation, the Gerdjikov–Ivanov (GI) equation, the modified Korteweg–de Vries equation and the Sharma–Tasso–Olever 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. 1、浏览全文需要使用软件--Abode Acrobat(由于软件较大并常见,我站不提供下载) 2、下载论文全文请点击(64KB)
本站收录的本文作者的其他论文: 1、The zero curvature representation for hierarchies of nonlinear evolution equations 2、Extended tanh-function method and its applications to nonlinear equations 3、Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation 5、Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method |
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