Nonlocality-induced front interaction enhancement

TL;DR

This paper shows that nonlocal coupling significantly enhances front interactions, alters their qualitative behavior, and can lead to the formation or destruction of localized structures in dynamical systems.

Contribution

It demonstrates how nonlocal interactions can dramatically amplify front velocities and induce qualitative changes in front dynamics, including oscillations and structure formation.

Findings

Nonlocal coupling amplifies front interaction strength.

Nonlocal terms induce oscillations in front profiles.

Nonlocal coupling can create or annihilate localized structures.

Abstract

We demonstrate that nonlocal coupling strongly influences the dynamics of fronts connecting two equivalent states. In two prototype models we observe a large amplification in the interaction strength between two opposite fronts increasing front velocities several orders of magnitude. By analyzing the spatial dynamics we prove that way beyond quantitative effects, nonlocal terms can also change the overall qualitative picture by inducing oscillations in the front profile. This leads to a mechanism for the formation of localized structures not present for local interactions. Finally, nonlocal coupling can induce a steep broadening of localized structures, eventually annihilating them.