非线性薛定谔方程的光纤解和调制不稳定性  

Optical Solutions and Modulation Instability of the Nonlinear Schr?dinger Equation

作　　者：秦春艳 QIN Chunyan(School of Mathematics and Statistics,Suzhou University,Suzhou 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《宿州学院学报》2021年第12期13-16,共4页Journal of Suzhou University

基　　金：安徽省高校自然科学研究项目(KJ2019A0666,KJ2019A0672);宿州学院重点科研项目(2020yzd06);宿州学院博士科研启动基金(2020BS011)。

摘　　要：非线性薛定谔方程不仅具有广泛的物理应用背景,而且在孤立子研究中具有十分重要的意义,它可以描述亮、暗孤立波解的传播现象。为更好地理解这些非线性现象,寻求它们的精确解,将孤子拟设法运用于非线性薛定谔方程,构造出它的两类光纤孤子解;基于双曲正切函数,通过计算得到该方程的复解;利用线性稳定性分析法,研究该模型的调制不稳定性。研究结果丰富了非线性薛定谔方程的非线性动态行为。The nonlinear Schr?dinger equation not only has a wide range of physical applications,but also has a very important significance in the study of solitons. It can describe the propagation phenomenon of bright and dark soliton solutions. In order to better understand these nonlinear phenomena,seek their exact solutions,the solitary ansatz method is applied to the nonlinear Schr?dinger equation and two kinds of soliton solutions are constructed. Based on the hyperbolic tangent function,the complexiton of the equation is obtained by calculation. The modulation instability of the model is studied by using linear stability analysis method. These results can enrich the nonlinear dynamic behavior of the nonlinear Schr?dinger equation.

关 键 词：非线性薛定谔方程 亮孤子解 暗孤子解 调制不稳定性 

分 类 号：O175.29[理学—数学]