用改进的试探函数法求解高维非线性演化方程

Solving Higher-dimensional Nonlinear Evolution Equations With the Improved Trial Function Method

将文献[10]中所提出的求非线性演化方程精确解的改进的试探函数法进行推广,求得了非线性数学物理中两个非常重要的高维非线性演化方程的精确解,包括一般形式的行波解、正则孤波解、奇异行波解等.本方法也可用于求解其它高维非线性演化方程.

In this paper, we generalize the improved trial function method for seeking the exact solutions of nonlinear evolution equations presented in Ref. [10] to obtain some exact solutions, comprising the general traveling wave solutions, the analytical solitary wave solutions and the singular traveling wave solutions, of two very important higher-dimensional nonlinear evolution equations in nonlinear mathematical physics. The technique used herein can be used to solve other higher-dimensional nonlinear evolution equations in nonlinear mathematical physics.