Topological Travelling Waves of a Macroscopic Swarmalator Model in Confined Geometries

We investigate a new class of topological travelling-wave solutions for a macroscopic 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. Both of them have non-trivial topology as their phases increase by a multiple of 2 π 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.