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Journal of Statistical Physics

, Volume 147, Issue 3, pp 506–518 | Cite as

Towards a Unified Method for Exact Solutions of Evolution Equations. An Application to Reaction Diffusion Equations with Finite Memory Transport

  • H. I. Abdel-Gawad
Article

Abstract

We present a brief report on the different methods for finding exact solutions of nonlinear evolution equations. Explicit exact traveling wave solutions are the most amenable besides implicit and parametric ones. It is shown that most of methods that exist in the literature are equivalent to the “generalized mapping method” that unifies them. By using this method a class of formal exact solutions for reaction diffusion equations with finite memory transport is obtained. Attention is focused to the finite-memory-transport-Fisher and Nagumo equations.

Keywords

Exact solutions Unified method Reaction diffusion equation Finite memory transport 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityCairoEgypt

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