ObjectiveIn recent years, due to the proposal of the theory of optical soliton communication, more and more researchers are paying attention to optical solitons. When a beam propagates in nonlinear medium, there will be dynamic competition between the diffraction effect of the beam and the self-focusing nonlinear effect, when the two effects achieve balance, a stable transmission state-optical soliton will be generated. Due to the stable transmission characteristics of optical solitons, they have bright development prospects and application potential in fields, such as fiber optic communication, optical information processing, and all optical switching. Therefore, it is necessary to explore the transmission characteristics of beams in different nonlinear systems.MethodsThe beam described by a special function provides new ideas for beam propagation due to its unique properties. Pearcey beams have attracted widespread attention due to their self-focusing, self-acceleration, and self-healing characteristics. Based on the nonlinear Schrödinger equation, the propagation dynamics of one-dimensional symmetric Pearcey-Gaussian beams in photorefractive media are studied numerically by using the split-step Fourier method. The split-step Fourier method, also be known as beam propagation method, has been used to solve many optical problems, such as wave propagation in the atmosphere, unstable resonators, waveguide couplers, gradient index fibers, and so on. The central idea of this method is to assume that diffraction and nonlinear effects act independently, thus obtaining an approximate result. The transmission process from z to z+h can be divided into two steps. The first step only considers nonlinear effects, and the second step only considers diffraction effects. Due to the fact that this method converts derivative operations in the time domain into product operations in the frequency domain, it is one to two orders of magnitude faster than most finite difference methods.Results and DiscussionsPhotorefractive medium is a medium that can produce light induced refractive index changes and is a weak light nonlinear effect medium. When incident light propagates in a photorefractive medium, the photorefractive material absorbs the light energy, and the migration of charges changes the refractive index of the photorefractive medium. When the focusing effect of the refractive index on the beam is balanced with the diffraction effect of the beam, optical solitons are formed. The results show that the beam can form breathing-like soliton or soliton pair under the nonlinear effect of photorefractive medium. With the nonlinear coefficient increasing, stable single-breathing soliton is gradually formed in photorefractive media. The distribution factor also affects the beam propagation. The larger the distribution factor is, the smaller period of the breathing soliton is and the larger frequency is. The larger initial amplitude will cause the beam to split during the evolution process and produce multiple sub-beams. The linear chirp affects the deviation angle of solitons, and the sign of chirp coefficient affects the deviation direction of solitons. The larger absolute value of chirp coefficient is, the larger deviation angle of solitons will be. The quadratic chirp affects the diffraction effect of the beam. The larger absolute value of the quadratic chirp coefficient is, the stronger the diffraction effect is.ConclusionsTherefore, we can control the transmission characteristics of symmetric Pearcey-Gaussian beams by changing the nonlinear coefficient of the photorefractive medium, the distribution factor, the initial amplitude and the chirp parameter of the initial input beam. The relevant research results enrich the content of nonlinear optical soliton transmission, and provide certain theoretical guidance for beam controls in optical systems.