非线性Schrdinger方程的对称约化和精确解

Symmetry Reduction and Exact Solutions of Nonlinear Schrdinger Equation

本文研究一类立方非线性Schrdinger方程的对称约化和精确解问题。首先,利用直接对称方法,得到非线性Schrdinger方程的对称;其次,根据求解相应的特征方程获得非线性Schrdinger方程的相似约化;最后,结合辅助方程获得非线性Schrdinger方程的精确解。这些解包括孤立波解、Jacobi椭圆函数解以及三角函数解。

Symmetry of nonlinear Schrdinger equation was investigated. Applying direct symmetry method,symmetry of nonlinear Schrdinger equation was derived. By solving corresponding characteristic equation associated with the symmetry equation,symmetry reduction of nonlinear Schrdinger were obtained based on a fourth- order auxiliary equation,these solutions include solitary wave solutions,Jacobi elliptic function solutions and trigonometric function solutions.