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We investigate the impact of nonlocality, owing to diffusive behavior, ontransverse instabilities of a dark stripe propagating in a defocusing cubicmedium. The nonlocal response turns out to have a strongly stabilizing effectboth in the case of a single soliton input and in the regime where dispersiveshock waves develop "multisoliton regime". Such conclusions are supported bythe linear stability analysis and numerical simulation of the propagation.

Suppression of transverse instabilities of dark solitons and their dispersive shock waves