Skip to main content
SpringerLink
Log in

Exact periodic wave solutions to the coupled Schrödinger-KdV equation and DS equations

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

The exact solutions for the coupled non-linear partial differential equations are studied by means of the mapping method proposed recently by the author. Taking the coupled Schrödinger-KdV equation and DS equations as examples, abundant periodic wave solutions in terms of Jacobi elliptic functions are obtained. Under the limit conditions, soliton 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. E J Parkes, B R Duffy and P C Abbott,Phys. Lett. A295, 280 (2002)

    ADS  MathSciNet  Google Scholar 

  2. E G Fan and J Zhang,Phys. Lett. A305, 383 (2002)

    ADS  MathSciNet  Google Scholar 

  3. S D Liu, Z T Pu, S K Liu and Q Zhao,Commun. Theor. Phys. 39, 167 (2003)

    Google Scholar 

  4. Y Z Peng,Chin. J. Phys. 41, 103 (2003)

    Google Scholar 

  5. Y Z Peng,J. Phys. Soc. Jpn. 72, 1356 (2003)

    Article  MATH  ADS  Google Scholar 

  6. Y Z Peng,Phys. Lett. A314, 401 (2003)

    ADS  Google Scholar 

  7. F Bowman,Introduction to elliptic functions with applications (Universities, London, 1959)

    Google Scholar 

  8. V Prasolov and Y Solovyev,Elliptic functions and elliptic integrals (American Mathematical Society, Providence, 1997)

    MATH  Google Scholar 

  9. S K Liu and S D Liu,Nonlinear equations in physics (Peking University Press, Beijing, 2000) (in Chinese)

    Google Scholar 

  10. C S Gardner, J M Green, M D Kruskal and R M Miura,Phys. Rev. Lett. 19, 1095 (1967)

    Article  MATH  ADS  Google Scholar 

  11. R Hirota,Phys. Rev. Lett. 27, 1192 (1971)

    Article  ADS  Google Scholar 

  12. P J Olver,Application of Lie group to differential equation (Springer, New York, 1986)

    Google Scholar 

  13. V B Matveev and M A Salle,Darboux transformations and solitons (Springer-Verlag, Berlin, 1991)

    MATH  Google Scholar 

  14. W Malfliet,Am. J. Phys. 60, 650 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  15. E J Parkes,J. Phys. A27, L497 (1994)

    ADS  MathSciNet  Google Scholar 

  16. E J Parkes and B R Duffy,Phys. Lett. A229, 217 (1997)

    ADS  MathSciNet  Google Scholar 

  17. B R Duffy and E J Parkes,Phys. Lett. A214, 271 (1996)

    ADS  MathSciNet  Google Scholar 

  18. E J Parkes, Z Zhu, B R Duffy and H C Huang,Phys. Lett. A248, 219 (1998)

    ADS  Google Scholar 

  19. T Yoshinaga, M Wakamiya and T Kakutani,Phys. Fluids A3, 83 (1991)

    ADS  Google Scholar 

  20. N N Rao,pramana — J. Phys. 29, 109 (1999)

    Google Scholar 

  21. S V Singh, N N Rao and P K Shukla,J. Plasma Phys. 60, 551 (1998)

    Article  ADS  Google Scholar 

  22. H Hase and J Satsuma,J. Phys. Soc. Jpn. 57, 679 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  23. A Davey and K Stewartson,Proc. R. Soc. London Ser. A338, 101 (1974)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, Henan University of Science and Technology, 471003, Luoyang, People’s Republic of China

    Yan-Ze Peng

Authors
  1. Yan-Ze Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan-Ze Peng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peng, YZ. Exact periodic wave solutions to the coupled Schrödinger-KdV equation and DS equations. Pramana - J Phys 62, 933–941 (2004). https://doi.org/10.1007/BF02706141

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02706141

Keywords

PACS Nos

Search

Navigation