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Wave pattern induced by a localized obstacle in the flow of a one-dimensional polariton condensate

Motivated by recent experiments on generation of wave patterns by a polariton condensate incident on a localized obstacle, we study the characteristics of such flows under the condition that irreversible processes play a crucial role in the system. The dynamics of a non-resonantly pumped polariton condensate in a quasi-one-dimensional quantum wire is modeled by a Gross-Pitaevskii equation with additional phenomenological terms accounting for the dissipation and pumping processes. The response of the condensate flow to an external potential describing a localized obstacle is considered in the weak-perturbation limit and also in the nonlinear regime. The transition from a viscous drag to a regime of wave resistance is identified and studied in detail.