Generation of dark solitons in oscillating Bose-Einstein condensates

We propose an experimentally tractable setting for observing an “instability” of a repulsive oscillating Bose-Einstein condensate that leads to the generation of dark solitons. We illustrate that when the trap of the condensate (which incorporates a localized impurity) is displaced so that the condensate flow is characterized by an atomic velocity larger than the local speed of sound, dark solitons are generated. The subcritical, near critical and supercritical are analyzed in detail.