Stable, mobile, dark-in-bright, dipolar Bose-Einstein-condensate solitons

We demonstrate robust, stable, mobile, quasi-one-dimensional, dark-in-bright dipolar Bose-Einsteincondensate (BEC) solitons with a notch in the central plane formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head-on collision of two such solitons is found to be quasielastic with practically no deformation. A proposal for creating dipolar dark-in-bright solitons in laboratories by phase imprinting is also discussed. A rich variety of such solitons can be formed in dipolar binary BECs, where one can have a dark-in-bright soliton coupled to a bright soliton or two coupled dark-in-bright solitons. The findings are illustrated using numerical simulation in three spatial dimensions by employing realistic interaction parameters for a dipolar Dy-164 BEC and a binary Dy-164-Dy-162 BEC.