Stable and mobile excited two-dimensional dipolar Bose-Einstein condensate solitons

We demonstrate robust, stable, mobile excited states of quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate (BEC) solitons for repulsive contact interaction with a harmonic trap along the $x$ direction perpendicular to the polarization direction $z$. Such a soliton can freely move in the y-z plane. A rich variety of such excitations is considered: one quanta of excitation for movement along (i) y axis or (ii) z axis or (ii) both. A proposal for creating these excited solitonic states in a laboratory by phase imprinting is also discussed. We also consider excited states of quasi-2D dipolar BEC soliton where the sign of the dipolar interaction is reversed by a rotating orienting field. In this sign-changed case the soliton moves freely in the x-y plane under the action of a harmonic trap in the $z$ direction. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The findings are illustrated using numerical simulation in three and two spatial dimensions employing realistic interaction parameters for a dipolar $^{164}$Dy BEC.