We demonstrate that the model of a spatially nonuniform two-component Bose-Einstein condensates (BEC) featuring the helicoidal spin-orbit coupling (SOC), gives rise to dark-bright soliton complexes characterized by spatiotemporal periodic oscillations in each component. These solitons are formed by the superposition of dark and bright ones, and exhibit a beating state over time and a striped state across space, earning them the designation of beating stripe solitons. Our analysis demonstrates that helicoidal SOC significantly affects the formation and dynamical properties of these solitons, also serving as the primary driver for spin oscillations. Through the nonlinear superposition of the beating stripe solitons, a range of intricate scenarios of the interaction between multiple solitons emerges, including head-on collisions, bound states, and parallel states.
We demonstrate exotic stable quasi-two-dimensional solitons in a Rashba or a Dresselhaus spin-orbit (SO)-coupled hyperfine spin-1 (
F=1) trapless antiferromagnetic Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, the solitons are of the $(\ensuremath{-}1,0,+1)$ or $(+1,0,\ensuremath{-}1)$ type with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, where the numbers in the parentheses denote the angular momentum in the spin components ${F}_{z}=+1,0,\ensuremath{-}1$, respectively. For intermediate SO coupling, the solitons have a multiring structure maintaining the above-mentioned vortices in the respective components. For larger SO coupling, superlattice solitons with a square-lattice structure in total density are found in addition to stripe solitons with a stripe pattern in the component densities with no periodic modulation in the total density.
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.