一类非线性发展方程的显式精确解

Explicit and Exact Solutions for a Type of Nonlinear Evolution Equation

文章推广了齐次平衡原则及F-展开法的思想,求得了含有参数的一类具有广泛物理背景的非线性发展方程utt-a1uxx+a2u+a3u3=0的显式精确解,其解主要包括Jacob i椭圆函数双周波期解、钟型孤波解和扭结型孤波解。用该方法求解不仅能获得一些新解而且方法简便,可以为求解其它类似的方程提供借鉴。

In this paper, the F-expansion and homogeneous method are used to solve a type of nonlin- ear evolution equation： utt-a1uxx＋a2u＋a3u^3=0. By means of the method, many kinds of explicit and exact traveling wave solutions are acquired, including Jacobian doubly periodic wave solutions, shock wave type solutions and bell wave type Solution. This method not only can obtained many new traveling wave solutions but also is very convenient, so it is worth being more extended.