三阶非线性薛定谔方程新的精确解

New Exact Solutions for a Third-order Schr?dinger Nonlinear Equation

三阶非线性薛定谔方程是描述光纤传输中光孤子演化的主要数学模型.为分析其演化规律,首先,通过包络孤立波变换把三阶非线性薛定谔方程化成一阶常微分方程组.然后,借助分支理论,得到系统平衡点、分支相图及演化轨道.同时也得到系统色散关系和Hamilton量.最后,沿不同的轨道积分得到演化方程各类孤波解,与原有解比较,得到了4个新解.

The third order nonlinear Schrodinger equation is the main mathematical model to describe the evolution of optical solitons in optical fiber transmission.To analyze its evolution rule,we transform the third order nonlinear Schr?dinger equation into a set of first order ordinary differential equations by means of envelope isolated wave transformation first.Then,with the help of the branching theory,the equilibrium point,the branching phase diagram and the evolution trajectory of the system are obtained.The system dispersion relation and Hamilton quantity are also obtained.Finally,various solitary wave solutions of the evolution equation are obtained by integrating along different orbitals,and four new solutions are obtained by comparing with the original solutions.