Dynamics of interacting Airy beams in the fractional Schrodinger equation with a linear potential

We investigate analytically and numerically the dynamics of interacting Airy beams in the fractional Schrodinger equation with a linear potential. It is shown that, for interaction of two Airy beams without the potential, the two components continue to diffract after collision when the Levy index alpha = 2, while symmetric splitting discrete diffraction-free beams are formed in the limiting case alpha = 1. With increasing the beams interval, the two main peaks split into four stronger diffraction-free beams, and there exist diffraction-free beams with weaker intensity between the two adjacent stronger diffraction-free beams for initial negative interval. If the external linear potential is considered, the interacting Airy beams exhibit a periodical modulated oscillation with a zigzag trajectory during propagation. The period is proportional to the absolute value of the potential depth coefficient. The propagation trajectory of the beams changes gradually from linear to parabolic when the Levy index increases. The propagation features of three interacting Airy beams are the same as that of two interacting Airy beams, but the propagation modes are different.