Self-focusing of plane dark solitons in nonlinear defocusing media

We analyze a transverse instability of plane (quasi-one-dimensional) dark solitons in the framework of the two-dimensional nonlinear Schrödinger (NLS) equation for beam propagation in a defocusing nonlinear medium. We show that in the vicinity of the instability threshold the exponential growth of transverse perturbations is stabilized by nonlinearity and also by the radiation emitted from the plane dark soliton to the right and left. Dynamics …