  The coupled-mode theory is developed for description of the nonlinear wave
dynamics in binary optical lattices. The obtained equations of motion
accurately describe nonlinear wave dynamics close to the band edges and in the
gap of the linear spectrum of the system. In order to demonstrate the power of
the presented approach, bright gap solitary wave solutions of the nonlinear
coupled- mode equations are derived and examined both analytically and
numerically. The presented results are relevant to nonlinear wave phenomena in
coupled waveguide arrays, coupled nano-cavities in photonic crystals,
metallo-dielectric systems, and the Bose-Einstein condensates in deep optical
lattices.
