  To show that steadily propagating nonlinear waves in active matter can be
driven internally, we develop a prototypical model of a topological kink moving
with a constant supersonic speed. We use a model of a bi-stable mass-spring
(FPU) chain capable of generating active stress. In contrast to subsonic kinks
in passive bi-stable chains, that are necessarily dissipative, the obtained
supersonic solutions are purely anti-dissipative. Our numerical experiments
point towards stability of the obtained kink-type solutions and the possibility
of propagating kink-anti-kink bundles reminiscent of solitons. We show that
even the simplest quasi-continuum approximation of the discrete model captures
the most important features of the predicted active phenomena.

Soft Condensed Matter