广义非线性薛定谔方程的新精确行波解

New Exact Solution to the Generalized Nonlinear Schrodinger Equation

利用符号运算方法研究了变系数薛定谔方程,对方程进行行波变换转化为常微分方程,分离实部和虚部并分别令为零,利用符号运算方法进行求解,获得了一系列带参数的精确行波通解,其中包括钟形孤子解,三角函数解,有理函数解,扭曲孤子解和Jacobi椭圆函数解。

The symbolic operation method is employed to construct new exact solutions of the generalized nonlinear Schrodinger equation. Firstly, the generalized nonlinear Schrodinger equation is converted into ordinary differential equation by traveling wave transform. Next, the real and imaginary parts of the ordinary differential equation are set to be zeros. Then, the ordinary differential equation is solved by the symbolic operation method. Finally, a series of new solutions have been constructed including Bell-shaped soliton solutions, trigonometric function solutions rational function solutions, twisted soliton solutions and Jacobi elliptic function solutions.