Skyrmion crystals in the pseudo-spin-1/2 Bose-Einstein condensates

Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose-Einstein condensates which are described by the coupled nonlinear Gross-Pitaevskii equations where the intraspecies and interspecies coupling constants are assumed to be equal. The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions. These stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, the crystal of skyrmion-antiskyrmion pairs is formed in the soliton limit.