Solitons in dipolar Bose-Einstein condensates with a trap and barrier potential

The propagation of solitons in the dipolar Bose-Einstein condensate 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 analysed analytically and numerically. Coherent splitting and fusion of the soliton by the defect are observed. The conditions for the fusion of split 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.