变系数非线性Schrdinger方程的孤子解及其相互作用

Solitons of nonlinear Schrdinger equation with variable-coefficients and interaction

在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrdinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrdinger方程转化成非线性Schrdinger方程,并利用已知解深入研究变系数非线性Schrdinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论.

Search for exact solutions to the generalized nonlinear Schrdinger equation is one of the essential directions in studies of the nonlinear dynamics in optical soliton and Bose-Einstein condensates.Stable soliton modes are of great significance for the experimental realization and potential application.In this paper,based on the introduction of a similarity transformation,the variable-coefficient nonlinear Schrdinger equation is transformed into the nonlinear Schrdinger equation,and then the single soliton solution,two-soliton solution and soliton solution in continuous-wave background for the variable coefficient nonlinear Schrdinger equation are obtained by using the known solutions.Meanwhile,their image analysis and relative discussion are given by selecting the different parameters in detail.