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Reductions and new exact solutions of the density-dependent Nagumo and Fisher equations

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Abstract

We show that conservation laws and their corresponding multipliers can be used to reformulate systems of partial differential equations and obtain some new classes of solutions. By applying the generalized double-reduction theorem to these systems via associated symmetries, one can construct exact solutions. This procedure is applied to specific cases of the density-dependent Nagumo and Fisher equations for which we obtain new solutions that differ in form from the well known analytic and numerical solutions.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3 Wits 2050, Johannesburg, South Africa

    P. Masemola & A. H. Kara

  2. Institut Matematik Kejuruteraan, Universiti Malaysia Perlis, 02000, Kuala Perlis, Perlis, Malaysia

    K. Fakhar

  3. Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310, UTM Skudai, Johor, Malaysia

    K. Fakhar

Authors
  1. P. Masemola
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  2. A. H. Kara
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  3. K. Fakhar
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Correspondence to A. H. Kara.

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Masemola, P., Kara, A.H. & Fakhar, K. Reductions and new exact solutions of the density-dependent Nagumo and Fisher equations. J Eng Math 82, 77–83 (2013). https://doi.org/10.1007/s10665-012-9591-8

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  • DOI: https://doi.org/10.1007/s10665-012-9591-8

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