扩展的Degasperis-Procesi方程的行波解分支
Traveling Wave Solutions and Bifurcations for Extended Degasperis-Procesi Equation
DOI: 10.12677/AAM.2021.102057, PDF,    科研立项经费支持
作者: 韦敏志：广西财经学院，广西 南宁；杨凤玲*：交通银行股份有限公司柳州分行，广西 柳州
关键词: 扩展的Degasperis-Procesi方程；动力系统分支理论；同宿轨；周期轨；行波解；Extended Degasperis-Procesi Equation； Bifurcation Theory of Dynamical Systems； Homoclinic Orbit； Periodic Orbit； Traveling Wave Solution
摘要: 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。
Abstract: 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.
文章引用：韦敏志, 杨凤玲. 扩展的Degasperis-Procesi方程的行波解分支[J]. 应用数学进展, 2021, 10(2): 531-536. https://doi.org/10.12677/AAM.2021.102057

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