非等谱散焦非线性Schrdinger方程的规范变换和精确解  

Gauge transformations and exact solutions of non-isospectral defocusing nonlinear Schrdinger equations

作　　者：孙君为[1] 张大军[1] 陈登远[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2013年第3期394-407,共14页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11071157);上海市教育委员会重点学科建设资助项目(J50101)

摘　　要：非线性Schrdinger方程及其相关方程在许多领域都得到广泛应用.为了研究谱参数随时间变化时散焦非线性Schrdinger方程的性质,研究了三个非等谱散焦非线性Schrdinger方程.对于前两个方程,给出了它们与等谱方程之间的规范变换,以及多孤子精确解.对于第三个方程给出了单孤子解.The nonlinear SchrSdinger equation and its relatives have been applied widely in variety of fields. Particularly, in recent years, the nonlinear SchrSdinger equation is used to model rogue waves which are the waves characterized by spa- tially and temporally localized amplitudes. In this paper, three non-isospectral defocusing nonlinear SchrSdinger equations are investigated corresponding to time- dependent spectral parameters that can lead to waves with time-dependent ampli- tudes. Among the three non-isospectral defocusing nonlinear SchrSdinger equa- tions, the first two are gauge equivalent to the isospectral defocusing nonlinear SchrSdinger equation. Therefore, their Lax pairs and exact soliton solutions are given via gauge transformations from those of the isospectral defocusing nonlinear SchrSdinger equation. For the third one, one of its soliton solutions is derived, and its dynamics is investigated.

关 键 词：非等谱散焦非线性Schrodinger方程 规范变换 精确解 

分 类 号：O175.29[理学—数学]