Abstract
A Theory is presented to construct several types of self-trapping nonlinear modes in the two-dimensional model of binary Bose-Einstein condensate (BEC) with the repulsive dipole-dipole interaction (DDI) and the spatially confined spin-orbit coupling (SOC). The spatially confined SOC can be induced by illuminating spinor BEC with a Gaussian beam. It is found that the two-dimensional SOC of Rashba type within a confined area can help trap the composite matter-wave solitons. Under the combined effects of the repulsive DDI and the SOC, stable solitons of semi-vortex type and mixed-mode type can be found in ground state as well as in excited state. These solitons can still be stable when the topological number is up to 11. The properties and stability of the nonlinear modes is also studied in a moving frame of reference.
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