By and large, optical "walking solitons" are localized, trapped short pulses or focused beams propagating in a nonlinear medium that, for whatever reason, may slow down or accelerate relative to the temporal or spatial group velocity of the frame of reference from where they are launched. They therefore "walk" off the corresponding temporal or spatial slot. Walking solitons might have all the possible shapes of known solitary waves—bright, dark, grey, or exotic—and propagate in any nonlinear material that allows the formation of solitary waves. However, their nature, properties, and overall relevance depend critically on the optical setting where they form, and on the mechanism that makes them walk.
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