On the geometric diversity of wavefronts for the scalar Kolmogorov ecological equation

In this work, we answer three fundamental questions concerning monostable travelling fronts for the scalar Kolmogorov ecological equation with diffusion and spatiotemporal interaction: these are the questions about their existence, uniqueness and geometric shape. In the particular case of the food-limited model, we give a rigorous proof of the existence of a peculiar, yet substantive non-linearly determined class of non-monotone and non-oscillating wavefronts. As regards to the scalar models coming from applications, this kind of wave solutions is analyzed here for the first time.