Multiring, stripe, and superlattice solitons in a spin-orbit-coupled spin-1 condensate

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 (-1,0,+1) or (+1,0,-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 Fz=+1,0,-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.