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Symmetry Reductions and Exact Solutions of a Generalized Fisher Equation

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Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 117))

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Abstract

In this chapter, we study a generalized Fisher equation based on the theory of symmetry reductions in partial differential equations. Optimal systems and reduced equations are obtained. We derive some travelling wave solutions by applying the (G'/G)-expansion method to one of these reduced equation.

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References

  1. Ablowitz, M.J., Zeppetella, A.: Bull. Math. Biol. 41, 835 (1979)

    Google Scholar 

  2. Britton, N.F.: Aggregation and the competitive exclusion principle. J. Theor. Biol. 136, 57–66 (1989)

    Article  MathSciNet  Google Scholar 

  3. Bruzon, M.S., Gandarias, M.L.: Symmetry reductions and travelling wave solutions for the Krichever-Novikov equation. Math. Methods Appl. Sci. 35(8):869–872 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cherniha, R., Serov, M., Rassokha, I.: Lie symmetries and form-preserving transformations of reaction diffusion convection equations. J. Math. Anal. Appl. 342, 136–3 (2008)

    Article  MathSciNet  Google Scholar 

  5. Gandarias, M.L., Bruzon, M.S., Rosa, M.: Nonlinear self-adjointness and conservation laws for a generalized Fisher equation. Commun. Nonlinear Sci. Numer. Simul. 18, 1600–1606 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kudryashov, N.A.: On “new travelling wave solutions” of the KdV and the KdV–Burgers equations. Commun. Nonl. Sci. Numer. Simulat. 14, 1891–1900 (2009)

    Google Scholar 

  7. Murray, J.D.: Mathematical Biology, 3rd edn. Springer, New York (2002)

    MATH  Google Scholar 

  8. Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer, Berlin (1986)

    Book  MATH  Google Scholar 

  9. Wang, M., Li, Xa., Zhang, J.: The (G'/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372, 417–423 (2008). doi: 10.1016/j.physleta.2007.07.051

    Google Scholar 

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Authors and Affiliations

  1. University of Cadiz Puerto Real, Puerto Real, Spain

    M. L. Gandarias, M. Rosa & M. S. Bruzon

Authors
  1. M. L. Gandarias
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  2. M. Rosa
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  3. M. S. Bruzon
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Corresponding author

Correspondence to M. L. Gandarias .

Editor information

Editors and Affiliations

  1. Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada

    Monica G. Cojocaru

  2. Dept of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Department of Mathematics and MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman N. Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roderick V. N. Melnik

  5. MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Hasan Shodiev

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Gandarias, M., Rosa, M., Bruzon, M. (2015). Symmetry Reductions and Exact Solutions of a Generalized Fisher Equation. In: Cojocaru, M., Kotsireas, I., Makarov, R., Melnik, R., Shodiev, H. (eds) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. Springer Proceedings in Mathematics & Statistics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-12307-3_31

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