Symbiotic solitons in quasi-one- and quasi-two-dimensional spin-1 condensates

We study the formation of spin-1 symbiotic spinor solitons in a quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) hyper-fine spin $F=1$ ferromagnetic Bose-Einstein condensate (BEC). The necessarily have repulsive intraspecies interaction are bound due to an attractive interspecies interaction. Due collapse instability higher dimensions, additional spin-orbit coupling is necessary stabilize quasi-2D soliton. Although quasi-1D soliton has simple Gaussian-type density distribution, novel spatial periodic structure found SO-coupled solitons. For weak SO coupling, $(-1, 0, +1)$ or $(+1, -1)$ type with intrinsic vorticity multi-ring structure, for Rashba Dresselhaus respectively, where numbers parentheses angular momenta projections components $F_z = +1, -1$, respectively. strong stripe superlattice solitons, square-lattice modulation density, addition stationary states were obtained by imaginary-time propagation mean-field model; dynamical stability was established real-time over long period time. possibility creation such removing trap confined BEC laboratory also demonstrated.