Nonlinear Excitations, Stability Inversions and Dissipative Dynamics in Quasi-one-dimensional Polariton Condensates

We consider the existence, stability and dynamics of the ground state and nonlinear excitations, in the form of dark solitons, for a quasi-one-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of remarkable features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates. For some sizeable parameter ranges, the nodeless ("ground") state becomes {\it unstable} towards the formation of {\em stable} nonlinear single or {\em multi} dark-soliton excitations. It is also observed that for suitable parametric choices, the instability of single dark solitons can nucleate multi-dark-soliton states. Also, for other parametric regions, {\em stable asymmetric} sawtooth-like solutions exist. Finally, we consider the dragging of a defect through the condensate and the interference of two initially separated condensates, both of which are capable of nucleating dark multi-soliton dynamical states.