分支方法与广义CH方程的显式周期波解  

Bifurcation Method and Explicit Periodic Wave Solutions to Generalized CH Equation

作　　者：刘正荣[1] Ali Mohammed Kayed 

机构地区：[1]华南理工大学数学科学学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2007年第10期227-232,共6页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571062);广东省自然科学基金资助项目(07006552)

摘　　要：用动力系统分支方法和数值模拟的方法去寻找广义CH方程的显式周期波解,首先建立与非线性偏微分方程对应的平面系统,其次绘制出该系统的的分支相图并做计算机数值模拟,确定分支相图中与显式周期波解有关的特殊轨道,最后通过这种特殊轨道及椭圆函数、椭圆积分来获得显式周期波解.Bifurcation method of dynamical systems and numerical simulation are used to look for the explicit periodic wave solutions to the generalized CH equation. First, the planar system corresponding to the nonlinear partial differential equation is established. Then, the bifurcation phase portraits of the traveling wave system are drawn, and the special orbits corresponding to the explicit periodic wave solutions are detected by numerical simulation. Fi- nally, via the special orbits, the elliptic functions and the elliptic integrals, the explicit periodic wave solutions are obtained.

关 键 词：非线性方程 分支 周期波解 孤立子 动力系统 

分 类 号：O175.12[理学—数学]