Title: Non-reciprocal topological solitons

Abstract: From protein motifs to black holes, topological solitons are pervasive nonlinear excitations that are robust and that can be driven by external fields. So far, existing driving mechanisms all accelerate solitons and antisolitons towards opposite directions. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators subject to a bistable potential. We find that such nonlinearity coaxes non-reciprocal excitations -- so-called non-Hermitian skin waves, which are typically unstable -- into robust oneway (anti)solitons. We rationalize our observations by introducing non-reciprocal generalizations of the Frenkel-Kontorova and sine-Gordon models, and use the latter to predict the terminal velocity of the (anti)solitons and determine their stability. Finally, we harness non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. More broadly, our findings suggest that non-reciprocal driving is a robust mechanism to steer nonlinear waves and could be generalized beyond mechanics, e.g. quantum mechanics, optics and soft matter.