Skip to main content
SpringerLink
Log in

Bifurcations of travelling wave solutions for generalized Drinfeld-Sokolov equations

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gurses M, Karasu A. Integrable KdV systems: recursion operators of degree four[J]. Phys Lett A, 1999, 251(4):247–249.

    Article  MathSciNet  Google Scholar 

  2. Hu Jianlan. A new method of exact travelling wave solution for coupled nonlinear differential equations[J]. Phys Lett A, 2004, 325(1):37–42.

    Article  MathSciNet  Google Scholar 

  3. Chow S N, Hale J K. Method of Bifurcation Theory[M]. Springer-Verlag, New York, 1981.

    Google Scholar 

  4. Guckenheimer J, Holmes P J. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[M]. Springer-Verlag, New York, 1983.

    Google Scholar 

  5. Li Jibin, Liu Zhengrong. Smooth and non-smooth travelling waves in a nonlinearly dispersive equation[J]. Appl Math Modelling, 2000, 25(1):41–56.

    Article  MATH  Google Scholar 

  6. Li Jibin, Liu Zhengrong. Travelling wave solutions for a class of nonlinear dispersive equations[J]. Chinese Ann Math Ser B, 2003, 23(3):397–418.

    Article  Google Scholar 

  7. Long Yao, Rui Weiguo, He Bin. Travelling wave solutions for a higher order wave equations of KdV type (I)[J]. Chaos, Solitons and Fractals, 2005, 23(2):469–475.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Honghe University, Mengzi, 661100, Yunnan Province, P. R. China

    Long Yao  (龙瑶) (Associate Professor), Rui Wei-guo  (芮伟国), He Bin  (何斌) & Chen Can  (陈灿)

Authors
  1. Long Yao  (龙瑶)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rui Wei-guo  (芮伟国)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. He Bin  (何斌)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chen Can  (陈灿)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Long Yao  (龙瑶).

Additional information

Communicated by LI Ji-bin

Project supported by the Key Project of Science Research Foundation of Educational Department of Yunnan Province, China (No.5Z0071A)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Long, Y., Rui, Wg., He, B. et al. Bifurcations of travelling wave solutions for generalized Drinfeld-Sokolov equations. Appl Math Mech 27, 1549–1555 (2006). https://doi.org/10.1007/s10483-006-1113-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-1113-1

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation