  We demonstrate the existence of a new class of two-component vector solitary
waves in which dispersion coefficients have of opposite signs. Stability is
achieved by inclusion of an additional linear coupling between the vector
components that counterbalances the instability produced by the mixed
dispersion and the non-linearity. In addition, we demonstrate that these
solutions are experimentally observable as gap vector solitons in Bose-Einstein
condensates located in oscillating optical lattices. The proposed experiment
falls well within the standard experimental procedures for generating gap
solitons in today's laboratories.
