A simple approach to the wave uniqueness problem

Abstract We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction–diffusion equations with distributed delay. This allows to solve an open problem concerning the uniqueness of non-monotone (hence, slowly oscillating) semi-wavefronts to the KPP–Fisher equation with delay. Similarly, a broad family of the Mackey–Glass type diffusive equations is shown to possess a unique (up to translation) semi-wavefront for each admissible speed.