A family of completely integrable multiHamiltonian systems explicitly related to some celebrated equations注意：本論文已在《JOURNAL OF MATHEMATICAL PHYSICS
VOLUME 42, NUMBER 9 SEPTEMBER 2001:43274344》發表 Engui Fan Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China ~Received 2 October 2000; accepted for publication 4 June 2001 By introducing a spectral problem with an arbitrary parameter, we derive a Kaup–Newelltype hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as the Kundu equation, the Kaup–Newell ~KN! equation, the Chen–Lee–Liu ~CLL! equation, the Gerdjikov–Ivanov ~GI! equation,the Burgers equation, the modified KortewegdeVries ~MKdV! equation and the Sharma–Tasso–Olver equation. It is shown that the hierarchy is integrable in Liouville’s sense and possesses multiHamiltonian structure. Under the Bargann constraint between the potentials and the eigenfunctions, the spectral problem is nonlinearized as a finitedimensional completely integrable Hamiltonian system. The involutive representation of the solutions for the Kaup–Newelltype hierarchy is also presented. In addition, an Nfold Darboux transformation of the Kundu equation is constructed with the help of its Lax pairs and a reduction technique. According to the Darboux transformation, the solutions of the Kundu equation is reduced to solving a linear algebraic system and two firstorder ordinary differential equations. It is found that the KN, CLL, and GI equations can be described by a Kundutype derivative nonlinear Schro¨dinger equation involving a parameter. And then, we can construct the Hamiltonian formulations, Lax pairs and Nfold Darboux transformations for the Kundu, KN, CLL, and GI equations in explicit and unified ways. 1、瀏覽PDF格式全文需要使用軟件－－Abode Acrobat(由于軟件較大并常見,我站不提供下載) 2、下載論文全文請點擊(113KB)
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