# Nonstandard quasi-monotonicity: an application to the wave existence in a neutral KPP-Fisher equation

## TL;DR

This paper extends the non-standard quasi-monotonicity method to prove the existence and uniqueness of monotone wavefronts in a neutral KPP-Fisher equation, advancing understanding of wave solutions in delayed reaction-diffusion systems.

## Contribution

It applies a novel quasi-monotonicity approach to a neutral KPP-Fisher equation, establishing both existence and uniqueness of monotone wavefronts, which was previously unresolved.

## Key findings

- Existence of monotone wavefronts in the neutral KPP-Fisher equation.
- Uniqueness (up to translation) of these wavefronts.
- Extension of the quasi-monotonicity method to neutral equations.

## Abstract

We revisit Wu and Zou non-standard quasi-monotonicity approach for proving existence of monotone wavefronts in monostable reaction-diffusion equations with delays. This allows to solve the problem of existence of monotone wavefronts in a neutral KPP-Fisher equation. In addition, using some new ideas proposed recently by Solar et al., we establish the uniqueness (up to a translation) of these monotone wavefronts.