  We study theoretically the emission of dark solitons induced by a moving
defect in a nonresonantly pumped exciton-polariton condensate. The number of
created dark solitons per unit of time is found to be strongly dependent on the
pump power. We relate the observed dynamics of this process to the oscillations
of the drag force experienced by the condensate. We investigate the stability
of the polariton quantum fluid and present various types of dynamics depending
on the condensate and moving obstacle parameters. Furthermore, we provide
analytical expressions for dark soliton dynamics using the variational method
adapted to the non-equilibrium polariton system. The determined dynamical
equations are found to be in excellent agreement with the results of numerical
simulations.
