  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.
