构造非线性波动方程孤波解的一种新方法

Study on soliton wave solutions of nonlinear wave equation with a new method

给出了构造非线性微分方程孤波解的一种方法,根据领头项分析,建立非线性微分方程与源方程一类特殊类型解的代数变换关系,利用该关系以及源方程的已知解,获得非线性微分方程的孤波解。用此方法构建了耦合KdV、KK、VB方程的孤波解。

This paper introduced a new approach for solving nonlinear partial differential equations. A simple algebraic transformation relation of a special type of solution was established between the nonlinear partial differential equation and the source equation by using leading analysis. With the aid of this relation and known solutions of the sorece equation,abundant soliton wave solutions were deri ved for the nonlinear partial differential equation. This method was applied to solve the couple KdV physi-cal model,KK system and VB equations.