Creation and Abrupt Decay of a Quasistationary Dark Soliton in a Polariton Condensate

We predict the existence of a self-localized solution in a nonresonantly pumped exciton-polariton condensate. The solution has a shape resembling the well-known hyperbolic tangent profile of a dark soliton, but exhibits several distinct features. We find that it performs small oscillations, which are transformed into ``soliton explosions'' at lower pumping intensities. Moreover, after hundreds or thousands of picoseconds of apparently stable evolution the soliton decays abruptly, which is explained by the acceleration instability found previously in the Bekki-Nozaki hole solutions of the complex Ginzburg-Landau equation. We show that the soliton can be formed spontaneously from a small seed in the polariton field or by using spatial modulation of the pumping profile.