Dynamics and stability of dark solitons in exciton-polariton condensates

We present a comprehensive analytical theory of localized nonlinear excitations---dark solitons---supported by an incoherently pumped, spatially homogeneous exciton-polariton condensate. We show that, in contrast to dark solitons in conservative systems, these nonlinear excitations ``relax'' by blending with the background at a finite time, which critically depends on the parameters of the condensate. Our analytical results for trajectory and lifetime are in excellent agreement with direct numerical simulations of the open-dissipative mean-field model. In addition, we show that transverse instability of quasi-one-dimensional dark stripes in a two-dimensional open-dissipative condensate demonstrates features that are entirely absent in conservative systems, as creation of vortex-antivortex pairs competes with the soliton relaxation process.