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Symmetry Reductions and Exact Solutions of a Generalized Fisher Equation

  • M. L. GandariasEmail author
  • M. Rosa
  • M. S. Bruzon
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 117)

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.

References

  1. 1.
    Ablowitz, M.J., Zeppetella, A.: Bull. Math. Biol. 41, 835 (1979)Google Scholar
  2. 2.
    Britton, N.F.: Aggregation and the competitive exclusion principle. J. Theor. Biol. 136, 57–66 (1989)MathSciNetCrossRefGoogle Scholar
  3. 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)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 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)MathSciNetCrossRefGoogle Scholar
  5. 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)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 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. 7.
    Murray, J.D.: Mathematical Biology, 3rd edn. Springer, New York (2002)zbMATHGoogle Scholar
  8. 8.
    Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer, Berlin (1986)zbMATHCrossRefGoogle Scholar
  9. 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.2007.07.051Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Cadiz Puerto RealPuerto RealSpain

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