Advertisement

Applied Mathematics and Mechanics

, Volume 28, Issue 7, pp 883–892 | Cite as

Kink wave determined by parabola solution of a nonlinear ordinary differential equation

  • Li Ji-bin  (李继彬)Email author
  • Li Ming  (黎明)
  • Na Jing  (纳静)
Article

Abstract

By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.

Key words

kink wave solution connecting orbit parabola solution nonlinear wave equation nonlinear evolution equation 

Chinese Library Classification

O175.12 

2000 Mathematics Subject Classification

34C25-28 58F05 58F14 58F30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Fan Engui. Uniformly constructing a series of explict exact solutions to nonlinear equations in mathematical physics[J]. Chaos, Solitons and Fractals, 2003, 16:819–839.zbMATHCrossRefGoogle Scholar
  2. [2]
    Li Jibin, Chen Guangrong. Bifurcations of travelling wave solutions for four classes of nonlinear wave equations[J]. Int J Bifucation and Chaos, 2005, 15(12):3973–3998.zbMATHCrossRefGoogle Scholar
  3. [3]
    Zhang Weiguo, Chang Qianshun, Jiang Baoguo. Explict exact solitary-wave solutions for compound KdV-type and compound KdV-Burgers equations with nolinear terms of any order[J]. Chaos, Solitons and Fractals, 2002, 13:311–319.zbMATHCrossRefGoogle Scholar
  4. [4]
    Parkes E J, Duffy B R. Travelling wave solutions to a compound KdV-Burgers equation[J]. Phys Letter A, 1997, 229:217–220.zbMATHCrossRefGoogle Scholar
  5. [5]
    Feng Zhaosheng. A note on “Explict exact solutions to the compound KdV equation”[J]. Phys Letter A, 2003, 312:65–71.zbMATHCrossRefGoogle Scholar
  6. [6]
    Li Biao, Chen Yong, Zhang Hongqing. Exact travelling wave solutions for a generalized Zakharov-Kuznetsov equation[J]. Appl Math Comput, 2003, 146:653–666.zbMATHCrossRefGoogle Scholar
  7. [7]
    Li Biao, Chen Yong, Zhang Hongqing. Explict exact solutions for some nolinear partial differential equations with nonlinear terms of any order[J]. Czech J Phys, 2003, 53:283–295.CrossRefGoogle Scholar
  8. [8]
    Liu Chunping. Exact analytical solutions for nonlinear reaction-diffusion equations[J]. Chaos, Solitons and Fractals, 2003, 18:97–105.zbMATHCrossRefGoogle Scholar
  9. [9]
    Wan X Y, Zhu Z S, Lu Y K. Solitary wave solutions of the generalized Burgers-Huxley equation[J]. J Phys A: Math Gen, 1990, 23:271–274.CrossRefGoogle Scholar
  10. [10]
    Chow S N, Hale J K. Method of bifurcation theory[M]. New York: Springer-Verlag, 1981.Google Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Li Ji-bin  (李继彬)
    • 1
    • 2
    Email author
  • Li Ming  (黎明)
    • 3
  • Na Jing  (纳静)
    • 4
  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaP. R. China
  2. 2.School of ScienceKunming University of Science and TechnologyKunmingP. R. China
  3. 3.Department of MathematicsQujing Normal InstituteQujingP. R. China
  4. 4.Computer Science DepartmentYunnan University of Finance and EconomicsKunmingP. R. China

Personalised recommendations