  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.
