非齐次光纤介质中孤子解和奇异波的特性研究  

Dynamics of the Soliton Solutions and Rogue Wave in the Nonhomogeneous Fiber Media

作　　者：薛慧 宋妮[1] 薛亚奎[1] XUE Hui;SONG Ni;XUE Ya-kui(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2020年第2期252-258,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11602232);山西省自然科学基金(201801D221040).

摘　　要：以非齐次光纤介质中的非线性薛定谔方程为研究对象,采用相似变换将变系数非线性薛定谔方程转化为标准非线性薛定谔方程,然后利用待定系数法求出方程的孤子解和奇异波解.基于该解表达式,选取不同类型函数和相应参数进行数值模拟,分析其动力学特性,所得结果对研究孤子在非齐次光纤介质中的传播具有重要意义.The nonlinear Schrodinger equation in the nonhomogeneous fiber media is studied.By using the idea of similarity transformation,the variable coefficient nonlinear Schrodinger equation is transformed into a standard nonlinear Schrodinger equation,and then the soliton solution and the rogue wave solution of the equation are obtained through the undetermined coefficient method.Based on the expressions form of the solutions,different types of functions and corresponding parameters are selected to simulate the image,and the dynamics of different solutions are realized and analyzed,which is very important to research the transmission of the soliton in the nonhomogeneous fiber media.

关 键 词：非线性薛定谔方程 相似变换 孤子解 奇异波 

分 类 号：O175.29[理学—数学]