Propagation and interaction of finite-energy Airy–Hermite–Gaussian beams in photorefractive media

We investigate numerically the propagation and interaction characteristics of finite-energy Airy–Hermite–Gaussian beams in biased photorefractive media. For the case of first-order Hermite polynomial, two main lobes of the initial input beam can form breathing solitons with two components. The interval between two soliton components in the \(y{\text{-direction}}\) increases gradually with the propagation distance, while the central position of two soliton components in the \(x{\text{-direction}}\) is almost unchanged during propagation. Moreover, in interaction situations, four main lobes of the two Airy–Hermite–Gaussian beams can also form breathing solitons with four components under the in-phase and out-of-phase conditions, respectively.