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

Abstract

The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds {Mathematical expression}. 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. © 1979 Society for Mathematical Biology.