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We investigate numerically interactions between two in-phase or out-of-phaseAiry beams and nonlinear accelerating beams in Kerr and saturable nonlinearmedia in one transverse dimension. We discuss different cases in which thebeams with different intensities are launched into the medium, but acceleratein opposite directions. Since both the Airy beams and nonlinear acceleratingbeams possess infinite oscillating tails, we discuss interactions betweentruncated beams, with finite energies. During interactions we see solitons andsoliton pairs generated that are not accelerating. In general, the higher theintensities of interacting beams, the easier to form solitons; when theintensities are small enough, no solitons are generated. Upon adjusting theinterval between the launched beams, their interaction exhibits differentproperties. If the interval is large relative to the width of the first lobes,the generated soliton pairs just propagate individually and do not interactmuch. However, if the interval is comparable to the widths of the maximumlobes, the pairs strongly interact and display varied behavior.

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media