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

We consider a generalized Fisher equation containing a spatial derivative t erm. Of interest is the question of the existence front solutions of the eq uation and their qualitative form. When the terms has a sufficiently small coefficient existence of such fronts is fourth-order of travelling fourth-o rder 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.