广义带导数的非线性Schrdinger方程的动态分析和精确解

Dynamic Analysis and Exact Solution of the General Nonlinear Schrdinger Equation With Derivative

利用动力系统方法,针对广义带导数的非线性Schrdinger方程的精确解问题进行研究分析.采用行波变换,将其化为常微分方程动力系统;计算出该方程动力系统的首次积分,讨论了系统在不同参数条件下的奇点与相图,得到对应的精确解,包括孤立波解、周期波解、扭结波解和反扭结波解.运用数值模拟的方法,对方程的光滑孤立波解和周期波解等进行了数值模拟.分析计算获得的结果完善了相关文献已有的研究成果.

With the dynamic system method,the qualitative performance and the exact solution of the general nonlinear Schrodinger equation with derivative were studied. Through the traveling wave transformation,the corresponding ordinary differential equation was deduced and the first integral was calculated.Under different parameter space conditions,the bifurcations of the general nonlinear Schrodinger equation with derivative were investigated,and the exact traveling wave solutions were obtained,such as solitary solutions,periodic solutions as well as kink and anti-kink solutions. The solitary wave solutions were considered through numerical simulation. The results show that the present findings improve the related previous conclusions.