# Multichromatic travelling waves for lattice Nagumo equations

## TL;DR

This paper investigates multichromatic traveling wave solutions in lattice Nagumo equations, revealing complex behaviors such as their emergence, disappearance, and interactions with monochromatic fronts as parameters vary.

## Contribution

It introduces the analysis of multichromatic fronts in lattice Nagumo equations, showing their dynamic existence and interactions, which were not previously understood.

## Key findings

- Multichromatic fronts can appear and vanish with changing diffusion.
- These fronts can travel alongside monochromatic fronts in certain regimes.
- Complex collision phenomena include wave reversal and transformation.

## Abstract

We discuss multichromatic front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatially heterogeneous $n$-periodic equilibria and hence are not monotonic like the standard monochromatic fronts. In contrast to the bichromatic case, our results show that these multichromatic fronts can disappear and reappear as the diffusion coefficient is increased. In addition, these multichromatic waves can travel in parameter regimes where the monochromatic fronts are also free to travel. This leads to intricate collision processes where an incoming multichromatic wave can reverse its direction and turn into a monochromatic wave.