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We numerically study the temporal evolution of a black-hole laserconfiguration displaying a pair of black and white hole horizons in a flowingatomic condensate. This configuration is initially prepared starting from ahomogeneous flow via a suitable space-dependent change of the interactionconstant and the evolution is then followed up to long times. Depending on thevalues of the system parameters, the system typically either converges to thelowest energy solution by evaporating away the horizons or displays acontinuous and periodic coherent emission of solitons. By making a physicalcomparison with optical laser devices, we identify the latter regime ofcontinuous emission of solitons as the proper black-hole laser effect. Weinclude some movies of the temporal evolution of the spatial density andvelocity profiles in the most significant cases.

Time-dependent study of a black-hole laser in a flowing atomic condensate