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We predict the existence of a self-localized solution in a nonresonantlypumped exciton-polariton condensate. The solution has a shape resembling thewell-known hyperbolic tangent profile of the dark soliton, but exhibits severaldistinct features. We find that it performs small oscillations, which aretransformed into 'soliton explosions' at lower pumping intensities. Moreover,after hundreds or thousands of picoseconds of apparently stable evolution thesoliton decays abruptly, which is explained by the acceleration instabilityfound previously in the Bekki-Nozaki hole solutions of the complexGinzburg-Landau equation. We show that the soliton can be formed spontaneouslyfrom a small seed in the polariton field or by using spatial modulation of thepumping profile.

Creation and abrupt decay of a quasi-stationary dark soliton in a polariton condensate