两类非线性波动方程的精确解

通过两种不同的方法求出了两类非一性波动方程的一些显式精确解。第一种方法是直接方法，第二种方法是直接方法和假设方法的一种结合。这两种方法都能精确求解两类非线性波动方程，得到的显式精确解包括钟状孤立波解、扭状孤立波解、两种类型的奇异行波解和４种类型的三角函数形周期波解。作为特例，可得到非一性的Ｐｏｃｈｈａｍｍｅｒ－Ｃｈｒｅｅ方程、对称的ｍＲＬＷ方程的显式精确解。

Exact Solutions for Two Classes of Nonlinear Wave Equations

Some explicit and exact travelling wave solutions for two classes of nonlinear wave equations are obtained by two different methods. The first method is a direct method. The second method is a combination of the direct method and the ansatze method. Each of these two methods is capable of solving these two nonlinear wave equations exactly. These explicit and exact solutions include the bell type solitary wave solutions, the kink type solitary wave solutions, the singular travelling wave solutions of two types, and the triangle function periodic wave solutions of four types. As the special cases, the exact and explicit solutions to the nonlinear Pochhammer Chree equation and the symmetric modified regularized long wave equation are obtained.