  The propagation of solitons in dipolar BEC in a trap potential with a barrier
potential is investigated. The regimes of soliton transmission, reflection and
splitting as a function of the ratio between the local and dipolar nonlocal
interactions are analyzed analytically and numerically. Coherent splitting and
fusion of the soliton by the defect is observed. The conditions for fusion of
splitted solitons are found. In addition the delocalization transition governed
by the strength of the nonlocal dipolar interaction is presented. Predicted
phenomena can be useful for the design of a matter wave splitter and
interferometers using matter wave solitons.
