含自相位调制非线性薛定谔方程的同伦分析

摘要

基于同伦分析方法研究了含自相位调制的非线性薛定谔方程。该方程可以用来描述光信号在光纤传输过程中因损耗、色散等导致的体系非线性效应。求出了方程的孤子解和周期解,并讨论了体系的二维和三维演化行为。This paper investigates the nonlinear Schrödinger equation with self-phase modulation based on the homotopy analysis method. This equation can be used to describe the nonlinear effects of the system caused by loss, dispersion, and other factors during optical signal transmission in optical fibers. The soliton solutions and periodic solutions of the equation are obtained, and the two-dimensional and three-dimensional evolution behaviors of the system are presented.