Nonadiabatic dynamics of dark solitons

We show that under certain conditions the dark soliton solutions of the defocusing nonlinear Schrr odinger equation can be less stable than their bright counterparts. This is due to the tendency of a dark soliton under external perturbation to generate dispersive waves that organize themselves in a \shelf" around the pulse wings, as exempliied by the simple case of dark solitons under small linear damping or ampliication. The shelf generation is a non-adiabatic process: the shelf area is of order unity after a propagation distance which scales like the inverse of the perturbation magnitude. This is in contrast with the bright soliton dynamics under similar circumstances. We analyze the impact of this extra source of dispersive waves on possible dark soliton-based long distance communication systems. We nd that the second order (in the normalized ampliier spacing) perturbation resulting from averagingg18, 19] does not lead to shelf formation, while a control devicee20] in general causes it, unless the controller parameters are chosen according to a simple criterion aimed at suppressing dispersive wave generation. We illustrate the eeectiveness of this criterion with extensive numerical simulations.