Advertisement

Applied Mathematics and Mechanics

, Volume 32, Issue 12, pp 1615–1622 | Cite as

Bifurcations of traveling wave solutions and exact solutions to generalized Zakharov equation and Ginzburg-Landau equation

  • Zhen-xiang Dai (戴振祥)
  • Yuan-fen Xu (徐园芬)Email author
Article

Abstract

This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given.

Key words

planar dynamical system periodic wave solution nonlinear wave equation 

Chinese Library Classification

O357.1 

2010 Mathematics Subject Classification

34C37 34C23 74J30 58Z05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Zhang, J. L., Wang, M. L., and Guo, K. Q. Exact solutions of generalized Zakharov and Ginzburg-Landau equations. Chaos, Solitons and Fractals, 32(5), 1877–1886 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    Zhang, W. G., Chang, Q. S., and Fan, E. G. Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order. Journal of Mathematical Analysis and Applications, 287(1), 1–18 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    Liu, C. S. Exact traveling wave solutions for a kind of generalized Ginzburg-Landau equation. Communications in Theoretical Physics, 43(5), 787–790 (2005)CrossRefMathSciNetGoogle Scholar
  4. [4]
    Li, J. B. and Chen, G. R. On a class of singular nonlinear traveling wave equations. International Journal of Bifuraction and Chaos, 17(11), 4049–4065 (2007)CrossRefzbMATHGoogle Scholar
  5. [5]
    Li, J. B. and Dai, H. H. On the Study of Singular Nonlinear Traveling Equations: Dynamical System Approach, Science Press, Beijing (2007)Google Scholar
  6. [6]
    Li, J. B., Wu, J. H., and Zhu, H. P. Travelling waves for an integrable higher order KdV type wave equations. International Journal of Bifurcation and Chaos, 16(8), 2235–2260 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    Byrd, P. F. and Fridman, M. D. Handbook of Elliptic Integrals for Engineers and Scientists, Springer, Berlin (1971)zbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Zhen-xiang Dai (戴振祥)
    • 1
  • Yuan-fen Xu (徐园芬)
    • 2
    Email author
  1. 1.School of Information and ArtNingbo Institute of EducationNingboZhejiang Province, P. R. China
  2. 2.Junior CollegeZhejiang Wanli UniversityNingboZhejiang Province, P. R. China

Personalised recommendations