  We investigate interactions by means of direct numerical simulations between
two finite Airy-Gaussian (AiG) beams in different media with the defected
photonic lattices in one transverse dimension. We discuss different lattice
structures in which the beams with different intensities and phases are
launched into the medium, but accelerate in opposite directions. During
interactions we see the interference fringe, breathers and soliton pairs
generated that are not accelerating. In the linear media, the initial
deflection direction of the accelerated beams is changed by adjusting the phase
shift and the beam interval. For a certain lattice period, the periodic
interference fringe can form. A constructive or destructive interference can
vary with the defect depth and phase shift. While the nonlinearity is
introduced, the breathers is generated. Especially, the appropriate beam
amplitude and lattice depth may lead to the formation of soliton pairs.
