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导数Schrodinger型方程族及其多Hamilton结构
注意:本论文已在《JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL》杂志2001年第34期513-519页发表
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范恩贵
(复旦大学 数学研究所,上海   200433

 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KNCLLGISTO 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KNCLLGI方程Lax对、Hamilton结构的统一、显式公式。
关键词
:方程族,Hamilton结构,Liouville可积

Integrable systems of derivative nonlinear Schr¨ odinger type and their multi-Hamiltonian structure

Engui Fan
JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL. 34(2001), 513-519

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.

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