扩展椭圆型辅助方程法与Klein-Gordon方程新解析解

The expansion auxiliary equation method of elliptic differential equation and solutions to nonlinear Klein-Gordon equation

利用辅助方程法,求解具有二阶非线性项Klein-Gordon方程,得到了大量精确解析解,其中包括孤波解和周期波解等,这些解对于研究二阶非线性项Klein-Gordon方程具有重要的指导意义.该方法具有普适性,可以用来寻找其他非线性发展方程的新精确解析解.

In this paper,the exact solutions to a new form nonlinear Klein-Gordon equation were found with the use of the auxiliary equation method based on mapping method,and the solitary solutions and periodic wave solutions were obtained.This method could also be used to explore exact solutions for other nonlinear evolution equations.