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Formation of oblique solitons by a flow of polariton condensate past anobstacle is considered. The flow is non-uniform due to a finite life-time ofpolaritons what changes drastically the conditions of formation of obliquesolitons compared with the atomic condensate case. The theory shows that thepolariton solitons can be generated by a subsonic flow in agreement with therecent experiment [A. Amo {\it et al.}, Science, {\bf 332,} 1167 (2011)].Geometric form of oblique solitons and other their parameters are calculatedanalytically and analytical results are confirmed by numerical simulations.

Oblique solitons in the flow of polariton condensate past an obstacle