The evolution of travelling waves in generalized Fisher equations via matched asymptotic expansions: Exponential corrections

In this paper we address an initial boundary value problem for a generalized Fisher equation. In particular we develop the matched asymptotic theory presented in Leach and Needham (2000) to consider the correction terms to the asymptotic approach to the wave-front of speed v = v*( 2) as t (time) . We establish the precise form of these corrections, and demonstrate that the rate of approach to the wave-front is algebraic in t when v* = 2 (there being two cases), but exponential in t when v* > 2.