Two aspects of the transport of the repulsive Bose-Einstein condensate (BEC) in a double-well trap are inspected: impact of the interatomic interaction and analogy to the Josephson effect. The analysis employs a numerical solution of 3D time-dependent Gross-Pitaevskii equation for a total order parameter covering all the trap. The population transfer is driven by a time-dependent shift of a barrier separating the left and right wells. Sharp and soft profiles of the barrier velocity are tested. Evolution of the relevant characteristics, involving phase differences and currents, is inspected. It is shown that the repulsive interaction substantially supports the transfer making it possible i) in a wide velocity interval and ii) three orders of magnitude faster than in the ideal BEC. The transport can be approximately treated as the d.c. Josephson effect. A dual origin of the critical barrier velocity (break of adiabatic following and d.c.-a.c. transition) is discussed. Following the calculations, robustness of the transport (d.c.) crucially depends on the interaction and barrier velocity profile. Only soft profiles which minimize undesirable dipole oscillations are acceptable.
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