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Abstract
The problem of the transcritical flow of a Bose-Einstein condensate through a wide
repulsive penetrable barrier is studied analytically using the combination of the
localized "hydraulic" solution of the 1D Gross-Pitaevskii equation and the solutions
of the Whitham modulation equations describing the resolution of the upstream and
downstream discontinuities through dispersive shocks. It is shown that within the
physically reasonable range of parameters the downstream dispersive shock is attached
to the barrier and effectively represents the train of very slow dark solitons, which
can be observed in experiments. The rate of the soliton emission, the amplitudes of
the solitons in the train and the drag force are determined in terms of the BEC oncoming
flow velocity and the strength of the potential barrier. A good agreement with direct
numerical solutions is demonstrated. Connection with recent experiments is discussed.