Skyrmion crystals in 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 intra-and inter-species 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. The stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, a crystal of skyrmion–anti-skyrmion pairs is formed in the soliton limit.