  Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic
function potential model a quasi one--dimensional interacting two-component
Bose-Einstein condensate trapped in a standing light wave. New families of
stationary solutions of the CNLS with a periodic potential are presented and
their stability studied by direct numerical simulations. Some of these
solutions allow reduction to Manakov system. From a physical point of view
these solutions can be interpreted as exact Bloch states at the edge of the
Brillouin zone. Some of them are stable while others are found to be unstable
against modulations of long wavelength. The solutions which are modulationally
unstable are shown to lead to the formation of localized ground states of the
coupled BEC system.
