Generation of breathing solitons in the propagation and interactions of Airy–Gaussian beams in a cubic–quintic nonlinear medium**Project supported by the National Natural Science Foundation of China (Grant No. 51602028), the Science and Technology Development Project of Jilin Province, China (Grant No. 20160520114JH), the Youth Science Fund of Changchun University of Science and Technology, China (Grant No. XQNJJ-2017-04), and the Natural

Abstract

Using the split-step Fourier transform method, we numerically investigate the generation of breathing solitons in the propagation and interactions of Airy–Gaussian (AiG) beams in a cubic–quintic nonlinear medium in one transverse dimension. We show that the propagation of single AiG beams can generate stable breathing solitons that do not accelerate within a certain initial power range. The propagation direction of these breathing solitons can be controlled by introducing a launch angle to the incident AiG beams. When two AiG beams accelerated in opposite directions interact with each other, different breathing solitons and soliton pairs are observed by adjusting the phase shift, the beam interval, the amplitudes, and the light field distribution of the initial AiG beams.