一类高次非线性方程的孤立波分支

Bifurcations of Solitary Waves for a Class of Higher Order Nonlinear Equations

本论文考虑一类含参数的高次非线性方程的孤立波分支,它们的行波系统都有一条奇直线。文章主要利用定性分析理论和动力系统分支方法,对方程次数为3和4的情形做出了研究,得出了各自情形下的分支波速、分支曲线以及孤立波的存在性和分支情况。

In this article, we consider the solitary wave bifurcation of a class of higher order nonlinear equations with parameter k, whose traveling wave system has a singular line. In this article, the qualitative analysis theory and the bifurcation method of dynamical system are used to study the case of equation with degree three and four, the bifurcation wave velocity, bifurcation curve and the existence and bifurcation of solitary wave are obtained.