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

## TL;DR

This paper investigates the existence, uniqueness, and geometric properties of wavefronts in the scalar Kolmogorov ecological equation, revealing a novel class of non-monotone, non-oscillating solutions especially in food-limited models.

## Contribution

It provides the first rigorous analysis of non-monotone, non-oscillating wavefronts in scalar ecological models with diffusion and spatiotemporal interaction.

## Key findings

- Existence of non-monotone, non-oscillating wavefronts in food-limited models
- Unique geometric shapes of wavefronts identified
- First analysis of such wave solutions in applied scalar models

## Abstract

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.