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導數Schrodinger型方程族及其多Hamilton結構
注意:本論文已在《JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL》雜志2001年第34期513-519頁發表
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(SCI收錄本文)

范恩貴
(復旦大學 數學研究所,上海   200433

 摘要:本文提出一個譜問題并由此導出一導數Schrodinger型方程族,證明了該方程族在Liouville意義下可積并擁有多Hamilton結構,發現幾類著名的方程,如KNCLLGISTO 方程等,均可做為特殊的約化包含在該方程族中,特別得到了KNCLLGI方程Lax對、Hamilton結構的統一、顯式公式。
關鍵詞
:方程族,Hamilton結構,Liouville可積

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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