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We investigate a new class of topological travelling-wave solutions for amacroscopipc swarmalator model involving force non-reciprocity. Swarmalatorsare systems of self-propelled particles endowed with a phase variable. Theparticles are subject to coupled swarming and synchronization. In previouswork, the swarmalator under study was introduced, the macroscopic model wasderived and doubly periodic travelling-wave solutions were exhibited. Here, wefocus on the macroscopic model and investigate new classes of two-dimensionaltravelling-wave solutions. These solutions are confined in a strip or in anannulus. 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 caseof the annulus) to the next. Existence and qualitative behavior of thesesolutions are investigated.

Topological travelling waves of a macroscopic swarmalator model in confined geometries