Journal of South China University of Technology (Natural Science Edition) ›› 2007, Vol. 35 ›› Issue (10): 227-232.

• Electronics, Communication & Automation Technology • Previous Articles    

Bifurcation Method and Explicit Periodic Wave Solutions to Generalized CH Equation

Liu Zheng-rong   Ali Mohammed Kayed   

  1. School of Mathematical Science , South China Univ. of Tech. , Guangzhou 510640 , Guangdong , China
  • Received:2007-03-01 Online:2007-10-25 Published:2007-10-25
  • Contact: 刘正荣(1955-) ，男，教授，博士生导师，主要从事动力系统和非线性微分方程研究 E-mail:liuzhr@ scut.edu. cn
  • About author:刘正荣(1955-) ，男，教授，博士生导师，主要从事动力系统和非线性微分方程研究
  • Supported by:

    国家自然科学基金资助项目(1 0571062) ;广东省自然科学基金资助项目(07006552)

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Abstract:

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. Finally, via the special orbits , the elliptic functions and the elliptic integrals , the explicit periodic wave solutions are obtained.

Key words: nonlinear equation, bifurcation, periodic wave solutions, soliton, dynamical system