Existence and construction of travelling wavefront solutions of Fisher equations with fourth-order perturbations

Abstract

We consider a generalized Fisher equation containing a fourth-order spatial derivative term. Of interest is the question of the existence of travelling front solutions of the equation and their qualitative form. When the fourth-order terms has a sufficiently small coefficient existence of such fronts is shown using invariant manifold theory. Asymptotic analysis is employed to construct an expression for the travelling front when its speed is large.