  We propose a spinning nonlinear resonator as an experimentally accessible
platform to achieve nonreciprocal control of optical solitons. Nonreciprocity
here results from the relativistic Sagnac-Fizeau optical drag effect, which is
different for pump fields propagating in the spinning direction or in the
direction opposite to it. We show that in a spinning Kerr resonator, different
soliton states appear for the input fields in different directions. These
nonreciprocal solitons are more stable against losses induced by inter-modal
coupling between clockwise and counterclockwise modes of the resonator. Our
work builds a bridge between nonreciprocal physics and soliton science,
providing a promising route towards achieving soliton-wave optical isolators
and one-way soliton communications.
