Skip to main content
SpringerLink
Log in

Application of Exp-function method to generalized Burgers-Fisher equation

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, the Exp-function method is used to construct exact solitary wave solutions for the generalized Burgers-Fisher equation with nonlinear terms of any order. With the aid of Maple computation, we obtain many new and more general exact solitary wave solutions expressed by various exponential and hyperbolic functions. Our results can successfully recover previously known solitary wave solutions that have been found by the tanh-function method and other more sophisticated methods.

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. Abolowitz, M.J., Clarkson, P.A. Solitons, nonlinear evolution equations and inverse scattering. Cambridge University Press, Cambridge, 1991

    Book  Google Scholar 

  2. Bekir, A., Boz, A. Application of Exp-function method for (2+1)-dimensional nonlinear evolution equations. Phys. Lett. A, 372: 1619–1628 (2008)

    Article  MathSciNet  Google Scholar 

  3. Ebaid, A. Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method. Phys. Lett. A, 365: 213–219 (2007)

    Article  MathSciNet  Google Scholar 

  4. EL-Wakil, S.A., Abdou, M.A. Modified extended tanh-function method for solving nonlinear partial differential equations. Chaos, Soliton and Fractals, 31: 1256–1264 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. EL-Wakil, S.A., Abdou, M.A. New exact travelling wave solutions for two nonlinear physical models. Nonlinear Analysis, 68: 35–46 (2008)

    Article  MathSciNet  Google Scholar 

  6. Fan, E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A, 277: 212–218 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. He, J.H., Wu, X.H. Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals, 30: 700–708 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kaya, D., EL-Sayed, S.M. A numerical simulation and explicit solutions of the generalized Burgers-Fisher equation. Appl. Math. Comput., 152: 403–413 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Moghimi, M., Hejazi, F.S.A. Variational iteration method for solving Generalized Burgers-Fisher and Burgers Equations. Chaos, Soliton and Fractals, 33: 1756–1761 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Parkes, E.J., Duffy, B.R. An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations. Comput. Phys. Commun., 98: 288–300 (1996)

    Article  MATH  Google Scholar 

  11. Peng, Y.J. Exact periodic wave solutions to a new Hamiltonian amplitude equation. Phys. Soc. Jpn, 72: 1356–1371 (2003)

    Article  MATH  Google Scholar 

  12. Wang, M.L. Exact solutions for a compound Kdv-Burgers equation. Phys. Lett. A, 213: 279–287 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Wazwaz, A.M. The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations. Appl. Math. Comput., 169: 321–338 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wu, X.H., He, J.H. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos, Solitons and Fractals, 34: 1421–1429 (2007)

    Article  MathSciNet  Google Scholar 

  15. Wu, X.H., He, J.H. Solitary solutions, periodic solutions and compacton-like solutions using the Expfunction method. Computers and Mathematics with Applications, 54: 966–986 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhang, S. Application of Exp-function method to a Kdv equation with variable coefficients. Phys. Lett. A, 365: 448–453 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Technology College, Southwest University of Science and Technology, Mianyang, 621010, China

    Zhen-hui Xu

  2. School of Science, Southwest University of Science and Technology, Mianyang, 621010, china

    Da-quan Xian

Authors
  1. Zhen-hui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Da-quan Xian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhen-hui Xu.

Additional information

Supported by the National Natural Science Foundation of China (No. 10971169).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, Zh., Xian, Dq. Application of Exp-function method to generalized Burgers-Fisher equation. Acta Math. Appl. Sin. Engl. Ser. 26, 669–676 (2010). https://doi.org/10.1007/s10255-010-0031-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-010-0031-0

Keywords

2000 MR Subject Classification

Search

Navigation