变系数非线性Schr(o)dinger方程的孤子解及其相互作用

摘要

Search for exact solutions to the generalized nonlinear Schrodinger 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 Schrodinger equation is transformed into the nonlinear Schrodinger equation, and then the single soliton solution, two-soliton solution and soliton solution in continuous-wave background for the variable coefficient nonlinear Schrodinger equation are obtained by using the known solutions. Meanwhile, their image analysis and relative discussion are given by selecting the different parameters in detail.%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(o)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(o)dinger方程转化成非线性Schr(o)dinger方程,并利用已知解深入研究变系数非线性Schr(o)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.