一个浅水波方程的精确解

The Explicit Solutions to a Shallow Wave Equation

通过考虑一个浅水波方程,介绍有关孤立子理论和Hirota方法,利用适当的变量代换,将孤立子方程化为双线性导数形式的微分方程,从方程的双线性导数形式出发,用摄动法得到孤立子方程的n-孤子解。

In this paper, by considering a shallow wave equation, we introduce the background knowledge about the soliton theory and the essentials of Hirota＇s method. Through a proper transformation , the soliton equation can be transformed into bilinear differential equations. Next, we obtained the exact n - soliton solution by the perturbation method.