Nonadiabatic dynamics of dark solitons

We show that under certain conditions the dark-soliton solutions of the defocusing nonlinear Schrödinger 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 into a shelf around the pulse wings, as exemplified by the simple case of dark solitons under small linear damping or amplification. The shelf generation is a nonadiabatic process: The shelf area is of order unity after a propagation distance that scales as the inverse of the perturbation magnitude. This is in contrast with the bright-soliton dynamics under similar circumstances. We analyze the effect of this extra source of dispersive waves on possible dark-soliton-based long-distance communication systems. We find that the second-order (in the normalized amplifier spacing) perturbation that results from averaging does not lead to shelf formation, whereas a control device in general causes it, unless the controller parameters are chosen according to a simple criterion aimed at suppressing dispersive wave generation. We illustrate the effectiveness of this criterion with extensive numerical simulations.