  We construct exact stationary solutions to the one-dimensional coupled
Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with
equal intraspecies and interspecies interaction constants. Three types of
complex solutions as well as their soliton limits are derived. By making use of
the SU(2) unitary symmetry, we further obtain analytical time-evolving
solutions. These solutions exhibit spatiotemporal periodicity.
