  Nonlinear wave patterns generated by the flow of polariton condensate past an
obstacle are studied for quasi-one-dimensional microcavity geometry. It is
shown that pumping and nonlinear damping play a crucial role in this process
leading to sharp differences in subsonic and supersonic regimes. Subsonic flows
result in a smooth disturbance of the equilibrium condensate around the
obstacle whereas supersonic flow generates a dispersive shock wave in the flow
upstream the obstacle and a long smooth downstream tail. Main characteristics
of the wave pattern are calculated analytically and analytical results are in
excellent agreement with the results of numerical simulations. The conditions
for existence of stationary wave patterns are determined numerically.
