利用MSE-法求Whitham-Broer-Kaup方程组的行波解

The traveling Solutions of the Coupled Whitham-Broer-Kaup Equations Using the Modified Simple Equation Method

通过对一个简单方程变形的方法,来构造数学物理与工程学中的非线性发展方程精确解的方法 (MSE),研究Whitham-Broer-Kaup方程组的行波解,得到了Whitham-Broer-Kaup方程组的几组新的更广义类型的精确解,其中包含一些新的孤立波解和周期波解.相比之前的求非线性发展方程精确解的方法,这种方法在精确解的构造过程中更具一般性,并且计算过程简单明了,不需要借助于任何复杂的符号计算软件.这一方法还可以被应用到其它非线性发展方程、常微分方程解的研究过程中.

Finding exact raveling wave solutions of nonlinear evolution equations（NLEE） in engineering and mathematical physics using the modified simple equation（MSE） method. By means of this scheme,several new kinds of generalized traveling solutions for the Coupled Whitham-Broer-Kaup Equations are obtained,which contain new solitary wave solutions and periodic wave solutions. Comparing the currently proposed method with other methods,this method is more general,and the process of the structuring of the exact solution and calculating is very simple and clear,without using the symbolic computation softwares. This method can also be applied to other nonlinear evolution equations and ordinary differential equations.