Interaction of Airy beams in a medium with parabolic potential

The interaction of the Airy beams in a medium with parabolic potential is investigated. It is found that the interaction of the two in-phase beams under the action of the parabolic potential can form the breathers, and the period will be affected by the depth of the potential. It's also notable that the interval and the phase play an important role in the interaction. In addition, the influences of the initial amplitudes of the two beams are also studied.