We study the formation of solitons in a uniform quasi-one-dimensional (quasi-1D) spin-orbit (SO) coupled self-repulsive pseudo spin-half and spin-one dipolar Bose-Einstein condensates (BEC), using the mean-field Gross-Pitaevskii equation. The dipolar atoms are taken to be polarized along the quasi-1D
x direction. In the pseudo spin-half case, for small SO-coupling, one can have dark-bright and bright-bright solitons. For large SO coupling, the dark-bright and bright-bright solitons may acquire a spatially-periodic modulation in density; for certain values of contact interaction paramerers there is only the normal bright-bright soliton without spatially-periodic modulation in density. In the spin-one anti-ferromagnetic case, for small SO coupling, one can have bright-bright-bright, dark-bright-dark, and bright-dark-bright solitons; and for large SO coupling, the dark-bright-dark and bright-dark-bright solitons are found to have spatially-periodic modulation in density. In the spin-one ferromagnetic case, for both small and large SO coupling, we find only bright-bright-bright solitons. All these solitons, specially those with a dark-soliton component, are dynamically stable as demonstrated by real-time propagation using the converged stationary solution obtained by imaginary-time propagation as the initial state.
We study the formation of solitons in a uniform quasi-two-dimensional (quasi-2D) spin-orbit (SO) coupled self-repulsive binary dipolar and nondipolar Bose-Einstein condensate (BEC) using the mean-field Gross-Pitaevskii equation. For a weak SO coupling, in a nondipolar BEC, one can have three types of degenerate solitons: a multiring soliton with intrinsic vorticity of angular momentum projection +1 or -1 in one component and 0 in the other, a circularly asymmetric soliton, and a stripe soliton with stripes in the density. For an intermediate SO coupling, the multiring soliton ceases to exist and a square-lattice soliton appears with a spatially periodic pattern in density on a square lattice, in addition to the degenerate circularly asymmetric and stripe solitons. In the presence of a dipolar interaction, with the polarization direction aligned in the quasi-2D plane, only the degenerate circularly asymmetric and stripe solitons appear.