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Explicit solutions of Fisher's equation for a special wave speed

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Abstract

The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds\(c = \pm 5/\sqrt {(6)} \). In this case the equation is shown to be of Painlevé type, i.e. solutions admit only poles as movable singularities. The general solution for this wave speed is found and a method is presented that can be applied to the solution of other nonlinear equations of biological and physical interest.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Clarkson College, 13676, Potsdam, New York, USA

    Mark J. Ablowitz & Anthony Zeppetella

Authors
  1. Mark J. Ablowitz
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  2. Anthony Zeppetella
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Ablowitz, M.J., Zeppetella, A. Explicit solutions of Fisher's equation for a special wave speed. Bltn Mathcal Biology 41, 835–840 (1979). https://doi.org/10.1007/BF02462380

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  • DOI: https://doi.org/10.1007/BF02462380

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