Skip to main content
SpringerLink
Log in

Topological Soliton and Other Exact Solutions to KdV–Caudrey–Dodd–Gibbon Equation

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

This paper studies the KdV–Caudrey–Dodd–Gibbon equation. The modified F-expansion method, exp-function method as well as the G′/G method are used to extract a few exact solutions to this equation. Later, the ansatz method is used to obtain the topological 1-soliton solution to this equation. The constraint conditions are also obtained that must remain valid for the existence of these solutions.

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. Abdollahzadeh M., Hosseini M., Ganbarpour M., Shirvani H.: Exact traveling wave solutions for fifth order Caudrey-Dodd-Gibbon equation. Int. J. Appl. Math. Comput. 2(4), 81–90 (2010)

    Google Scholar 

  2. Cao C., Wu Y., Geng X.: On quasi-periodic solutions of the Caudrey-Dodd-Gibbon-Kotera-Sawada equation. Phys. Lett. A 256(1), 59–65 (1999)

    Article  Google Scholar 

  3. Chan W.L., Zheng Y-K.: Bäcklund transformations for the Caudrey-Dodd-Gibbon-Kotera-Sawada equation and its λ-modified equation. J. Math. Phys. 30(9), 2065 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hu X-B., Li Y.: Some results on the Caudrey-Dodd-Gibbon-Kotera-Sawada equation. J. Phys. A 24, 3205–3212 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jiang B., Bi Q.: A study on the bilinear Caudrey-Dodd-Gibbon equation. Nonlinear Anal. Theory Methods Appl. 72(12), 4530–4533 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lou S-Y.: Twelve sets of symmetries of the Caudrey-Dodd-Gibbon-Kotera-Sawada equation. Phys. Lett. A 175(1), 23–26 (1993)

    Article  MathSciNet  Google Scholar 

  7. Rogers C., Carillo S.: On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kuperschmidt hierarchies. Phys. Scr. 36, 865–869 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wazwaz A-M.: N-soliton solutions for the combined KdV-CDG and the KdV-Lax equation. Appl. Math. Comput. 203(1), 402–407 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wazwaz A-M.: Multiple soliton solutions for the (2+1)-dimensional Sawada-Kotera and Caudrey-Dodd-Gibbon (CDG) equations. Math. Methods Appl. Sci. 34(13), 1580–1586 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Xu Y-G., Zhou X-W., Yao L.: Solving the fifth order Caudrey-Dodd-Gibbon (CDG) equation using exp-function method. Appl. Math. Comput. 206(1), 70–73 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA

    Anjan Biswas

  2. Department of Mathematical Sciences, University of Tabriz, 51666-14766, Tabriz, Iran

    Ghodrat Ebadi & Nazila Yousefzadeh

  3. Radiation Physics Laboratory, Department of Physics, Badji Mokhtar University, 2300, Anaba, Algeria

    Houria Triki

  4. Department of Mathematics, Ege University, 35100, Bornova, Izmir, Turkey

    Ahmet Yildirim

  5. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Ahmet Yildirim

Authors
  1. Anjan Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghodrat Ebadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Houria Triki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ahmet Yildirim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nazila Yousefzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmet Yildirim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Biswas, A., Ebadi, G., Triki, H. et al. Topological Soliton and Other Exact Solutions to KdV–Caudrey–Dodd–Gibbon Equation. Results. Math. 63, 687–703 (2013). https://doi.org/10.1007/s00025-011-0226-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-011-0226-6

Mathematics Subject Classification (2010)

Search

Navigation