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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt

    H. I. Abdel-Gawad

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  1. H. I. Abdel-Gawad
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Correspondence to H. I. Abdel-Gawad.

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Abdel-Gawad, H.I. Towards a Unified Method for Exact Solutions of Evolution Equations. An Application to Reaction Diffusion Equations with Finite Memory Transport. J Stat Phys 147, 506–518 (2012). https://doi.org/10.1007/s10955-012-0467-0

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  • DOI: https://doi.org/10.1007/s10955-012-0467-0

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