Solitons on oscillating and rotating backgrounds

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Abstract
We show that kink solitons may exist on top of a rotating background as localized objects if the background dynamics is phase locked to a rapidly oscillating ac force. The result is demonstrated analytically for the sine-Gordon model, showing excellent agreement with numerical simulations. In the context of long Josephson junctions this phenomenon means that the well known Shapiro steps in the current-voltage characteristics change into a set of the zero-field steps according to the number of propagating fluxons.