扩展的Degasperis-Procesi方程的行波解分支

Traveling Wave Solutions and Bifurcations for Extended Degasperis-Procesi Equation

Degasperis-Procesi方程是偏微分方程中非常重要的一个方程。本文主要介绍扩展的Degasperis-Procesi方程,利用行波变换将偏微分方程转换成常微分方程,再对方程中的参数进行分析得到相图分支,根据相图轨道构建出方程精确行波解,求出其参数表达式。同时证明了在某些参数条件下,扩展的Degasperis-Procesi方程具有光滑的孤立波解和周期波解。

Degasperis-Procesi equation is one of the most important partial differential equations. The presented paper mainly introduces the extended Degasperis-Procesi equation. The partial differential equation is transformed into ordinary differential equation by traveling wave transformation, and then the parameters in the formula are analyzed to obtain the phase diagram branch. According to the phase diagram orbit, the exact traveling wave solutions for the equation are constructed. It is proved that the extended Degasperis-Procesi equation has smooth solitary wave solution and periodic wave solution under some certain parametric conditions.