摘要:
本文主要用行波法来求解一类带有导数项非线性薛定谔方程的行波解。首先通过引入行波变换
，将非线性的偏微分方程化为常微分方程组，进一步得到哈密尔顿系统，通过讨论一元三次方程根的情况对其表达式进行化简。然后借助软件求解方程，得到原方程行波解的函数解析式并结合图像，较为清晰地展现其波形。
Abstract:
This paper mainly uses the traveling wave method to solve a nonlinear Schrodinger equation with derivative term for its travelling wave solutions. Firstly, one introduces a travelling wave transformation
to transform the nonlinear Schrodinger equation into the ordinary differential equations; the Hamilton system is further obtained. In the process of getting the travelling wave solutions, the roots of simple Cubic Equations are discussed to simplify a Cubic expression. Then, one obtains some analytical solutions. Lastly, one presents clearly the travelling wave from the graphs of the solutions.