Topological travelling waves of a macroscopic swarmalator model in confined geometries

TL;DR

This paper explores novel topological travelling-wave solutions in a macroscopic swarmalator model with non-reciprocal forces, focusing on confined geometries like strips and annuli, revealing solutions with non-trivial phase topology.

Contribution

It introduces new classes of topological travelling-wave solutions in a macroscopic swarmalator model within confined geometries, expanding understanding of their existence and behavior.

Findings

Existence of topological travelling waves in confined geometries.

Solutions exhibit phase changes of multiples of 2π across periods.

Qualitative analysis of solution behavior in strips and annuli.

Abstract

We investigate a new class of topological travelling-wave solutions for a macroscopipc swarmalator model involving force non-reciprocity. Swarmalators are systems of self-propelled particles endowed with a phase variable. The particles are subject to coupled swarming and synchronization. In previous work, the swarmalator under study was introduced, the macroscopic model was derived and doubly periodic travelling-wave solutions were exhibited. Here, we focus on the macroscopic model and investigate new classes of two-dimensional travelling-wave solutions. These solutions are confined in a strip or in an annulus. In the case of the strip, they are periodic along the strip direction. They have non-trivial topology as their phase increases by a multiple of $2 \pi$ from one period (in the case of the strip) or one revolution (in the case of the annulus) to the next. Existence and qualitative behavior of these solutions are investigated.