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

In this paper we address an initial-boundary-value problem for a generalized Fisher equation. In particular, we use the method of matched asymptotic expansions to develop a rational approach for determining the propagation speed for the large-t(time) travelling wave structures which evolve in the initial-boundary-value problem. This approach resolves apparent paradoxes which arise in the much used linearized approximation (in the cases R(u) ⩽ uand R(u) ≰ u, where R(u)is the associated reaction function) and is readily adaptable to systems of Fisher–Kolmogorov type and to problems in higher spatial dimensions.