双组份Degasperis-Procesi方程的有界行波解  

Bounded Traveling Wave Solutions for the Two Component Degasperis-Procesi Equation

作　　者：余丽琴[1] 田立新[1] 

机构地区：[1]江苏大学非线性科学研究中心,镇江212013

出　　处：《工程数学学报》2013年第3期407-415,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11171135);江苏大学高级人才基金(12JDG102)~~

摘　　要：本文研究双组分Degasperis-Procesi方程的有界行波解.利用平面动力系统的分岔理论,分析了双组分Degasperis-Procesi方程对应行波系统在参数平面不同区域的分岔相图.进而,依据动力系统相轨中的同宿轨、周期轨与非线性波动方程的孤立波解、周期波解之间的关系,在一定的参数条件下,获得了双组份Degasperis-Procesi方程的孤立波解和周期波解,并借助数值模拟给出了部分解的图像.The paper investigates the bounded traveling wave solutions for the two component Degasperis-Procesi equations. By using the bifurcation theory of planar dynamical systems, we analyze the bifurcation phase portraits of the traveling wave system corresponding to the two component Degasperis - Procesi equations in the different regions of parameter spaces. More- over, according to the relationship among homoclinic orbits, periodic solutions, solitary wave solutions and periodic wave solutions of nonlinear wave equations, solitary wave solutions and periodic wave solutions are obtained under some parameter conditions. Finally, numerical sim- ulations are given for some solutions.

关 键 词：双组份Degasperis-Procesi方程 动力系统的分岔理论 有界行波解 

分 类 号：O175.14[理学—数学]