A Multi-Soliton Solution of the DNLS Equation Based on Pure Marchenko Formalism  

作　　者：ZHOU Guoquan School of Physics and Technology,Wuhan University,Wuhan 430072,Hubei,China 

出　　处：《Wuhan University Journal of Natural Sciences》2010年第1期36-42,共7页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (10775105)

摘　　要：By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one-and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile,the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process（from t →∞ to t → ＋∞ ） of the elastic collisions.By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one-and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile,the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process（from t →∞ to t → ＋∞ ） of the elastic collisions.

关 键 词：SOLITON derivative nonlinear Schrdinger （DNLS） equation nonlinear equation Marchenko equation 

分 类 号：O413.1[理学—理论物理] TN929.11[理学—物理]