Bulletin of Mathematical Biology

, Volume 41, Issue 6, pp 835–840

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

  • Mark J. Ablowitz
  • Anthony Zeppetella

DOI: 10.1007/BF02462380

Cite this article as:
Ablowitz, M.J. & Zeppetella, A. Bltn Mathcal Biology (1979) 41: 835. doi:10.1007/BF02462380


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.

Copyright information

© Society for Mathematical Biology 1979

Authors and Affiliations

  • Mark J. Ablowitz
    • 1
  • Anthony Zeppetella
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson CollegePotsdamUSA

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