Papers › Topological travelling waves of a macroscopic swarmalator model in confined geometries
Topological travelling waves of a macroscopic swarmalator model in confined geometries
Pierre Degond, Antoine Diez
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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 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.
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