一些非线性发展方程的有界钟状代数孤立波解

Bounded Bell Shape Algebraic Solitary Wave Solutions of Some Nonlinear Evolution Equations

本文以非线性发展方程的有界钟状代数孤波解为研究对象,以Kolmogorov-Petrovskii-Piskunov(简称KPP)方程、组合KdV-mKdV方程和mKdV方程为例,利用平面动力系统知识,分析有界钟状代数孤立波解出现的条件,提出求解的方法,称之为代数孤波解解法(简称ASW解法),分别获得这三个方程的代数孤立波解.

The bounded bell shape algebraic solitary wave solutions of nonlinear evolution equations are researched in this paper. The Kolmogorov-Petrovskii-Piskunov （KPP for short） equation,compound KdV-mKdV equation and mKdV equation are chose to as examples. The theory of planar dynamical systems is applied to study the existence conditions of algebraic solitary wave solutions. The algebraic solitary wave solutions of these three equations are ob- tained respectively. And a method for solving this type solutions is proposed, which is called algebraic solitary wave solution method（ASW method for short）.