非线性薛定谔方程的精确解析解  

Exact analytical solutions for the nonlinear Schrödinger equation

作　　者：赵欢[1] Zhao Huan(Nanchang Institute of Technology,Nanchang 330044,China)

机构地区：[1]南昌理工学院,江西南昌330044

出　　处：《南昌大学学报（理科版）》2021年第2期116-119,共4页Journal of Nanchang University(Natural Science)

基　　金：江西省高校人文社会科学研究(GL20133)。

摘　　要：薛定谔方程可以用来描述具有非线性和分布色散的非均匀光纤中孤子传输的动力学。本文获得了变系数非线性薛定谔方程大量的精确解析解,包括了亮孤子解、暗孤子解、双曲函数解、三角函数解以及一些有理解。这些解有丰富的动力学结构,有助于我们理解薛定谔方程背后的物理背景。The Schrödinger equation can be used to describe the dynamics of soliton propagation in inhomogeneous fibers with nonlinear and distributed dispersion.In this paper,a large number of exact analytical solutions of nonlinear Schrödinger equation with variable coefficients are obtained,including bright soliton solution,dark soliton solution,hyperbolic function solution,trigonometric function solution and some understandings.These solutions have rich dynamic structures and they can help us understand the physical background behind the Schrödinger equation.

关 键 词：薛定谔方程 亮暗孤子解 双曲函数解 三角函数解 

分 类 号：O175.11[理学—数学]