Anisotropic solitary semivortices in dipolar spinor condensates controlled by the two-dimensional anisotropic spin-orbit coupling

We study families of anisotropic solitary semivortices (SVs) in spinor dipolar Bose-Einstein condensates (BECs), with two localized components linearly mixed by the two-dimensional anisotropic spin-orbit (SO) coupling of the Rashba type. The intrinsic nonlinearity of this system represented by the anisotropic dipole-dipole interactions (DDIs) between atomic magnetic moments is aligned parallel to the system's plane by an external magnetic field. The affects of the anisotropic SO-coupling and the interplay between SO-coupling and DDI to the solitons of the SV type are systematically studied through the paper. For the SVs, we demonstrate that the shape of the vortex component, which is vertical or horizontal anisotropic solitary vortices (ASV) with respect to the in-plane polarization of the atomic dipole moments in the underlying BEC, may be effectively controlled by the anisotropy degree, λx/λy, of the SO-coupling. A novel type of ASV, elliptical ring shaped vortices, is found at the transition point between the horizontal and vertical shapes. Such ASV contains the largest value of the average angular momentum. Influences of the anisotropic SO-coupling to the mobility of the SV are studied by the direct simulation to the kicked soliton on the x and y directions. Trajectories of the kicked soliton show a strong anisotropy which depends on the anisotropy degree of the SO-coupling.