Skip to main content
SpringerLink
Log in

A new method for finding special solutions of nonlinear diffusion equation

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

A straightforward and concise method is proposed to construct special solutions of nonlinear diffusion equation. Many new special solutions obtained. We believe this method is effective on solving other nonlinear differential equations.

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. Dorodnitsyn, V.A., Knyazeva, I.V., Svirshchevskii, S.R.: The group properties of heat equation with source in two and three-deminsional case. Differ. Equ. 19, 1215–1223 (1983)

    MathSciNet  Google Scholar 

  2. Galaktionov, V.A.: Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearties. Proc. R. Soc. Edinb. 125A, 225–246 (1995)

    MathSciNet  Google Scholar 

  3. Clarkson, P.A., Mansfield, E.L.: Symmetry reductions and exact solutions of a class of nonlinear heat equations. Physica D 70, 250–288 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fushchych, W.I., Serov, N.I., Tulupova, L.A.: The conditional invariance and exact solutions of the nonlinear diffusion equation. Proc. Acad. Sci. Ukraine 4, 37–40 (1993)

    Google Scholar 

  5. Ovsiannikov, L.V.: Group Analysis of Differential Equations. Academic Press, New York (1982)

    MATH  Google Scholar 

  6. Bluman, G.W., Cole, J.: The general similarity solutions of the heat equation. J. Math. Mech. 18, 1025–1042 (1969)

    MATH  MathSciNet  Google Scholar 

  7. Bluman, G.W., Kumei, S.: On the remarkable nonlinear diffusion equation. J. Math. Phys. 21, 1019–1023 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gandarias, M.L.: New symmetries for a model of fast diffusion. Phys. Lett. A 286, 153–160 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Popovych, R.O., Vaneeva, O.O., Ivanova, N.M.: Potential nonclassical symmetries and solutions of fast diffusion equation. Phys. Lett. A 362, 166–173 (2007)

    Article  MathSciNet  Google Scholar 

  10. Ibragimov, N.H. (ed.): Lie Group Analysis of Differential Equations Symmetries, Exact Solutions and Conservation Laws, vols. 1–3. Chemical Rubber Company, Boca Raton (1994–1996)

    Google Scholar 

  11. Kaptsov, O.V., Verevkin, I.V.: Differential constraints and exact solutions of nonlinear diffusion equations. J. Phys. A: Math. Gen. 36, 1401–1414 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kaptsov, O.V., Schmidt, A.V.: Linear determining equations for differential constraints. Glasgow Math. 47A, 109–120 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ames, W.F.: Nonlinear Partial Differential Equations in Engineering, vol. 2. Academic Press, New York (1972)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Math & Statistics College, Chongqing Technology and Business University, Chongqing, 400067, China

    Maochang Qin

  2. Math & Stats Dept., McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    Guihong Fan

Authors
  1. Maochang Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guihong Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maochang Qin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qin, M., Fan, G. A new method for finding special solutions of nonlinear diffusion equation. Nonlinear Dyn 55, 349–353 (2009). https://doi.org/10.1007/s11071-008-9368-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-008-9368-9

Keywords

Search

Navigation