一类广义K(m,n)方程的行波解

Traveling wave solutions to a class of generalized K(m,n)equations

运用微分方程定性理论和动力系统分支方法,研究了一类广义K(m,n)方程的行波解。考虑了两种情形:K(1,3,2)方程和K(2,3,3)方程。在不同的参数条件下,得到K(1,3,2)方程的紧孤子和K(2,3,3)方程的紧孤子及周期爆破波解。进一步通过数值模拟,分析其系统的分支相图和行波解的波形图。

This article studied traveling wave solutions to the generalized K(m,n)equations by the qualitative theory of differential equations and the bifurcation method of dynamical systems.Two cases are considered:the K(1,3,2)equation and the K(2,3,3)equation.Under the different parameter conditions,compactons of the K(1,3,2)equation are derived,compactons and periodic blow-up wave solutions of the K(2,3,3)equation are obtained.The bifurcation phase of the plane system and the figure of traveling wave solutions are analyzed by numerical simulations.