Bound states of breathing Airy–Gaussian beams in nonlocal nonlinear medium

•The propagation dynamics of a single Airy–Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations are studied.•With the split-step Fourier method, numerical results shows that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states.•To the formation of stable bound states, the smaller the interval of the two AiG beams, the stronger the attraction and the smaller the period of AiG breathing to the in-phase case.•By tuning the phase difference between the two beams, we can steer the center of the bound AiG beams in nonlocal nonlinear media.

With a nonlocal model, we investigate the propagation dynamics of a single Airy–Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results shows that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Especially, by tuning the phase difference between the two beams, we can steer the center of the bound AiG beams in nonlocal nonlinear media.