The Airyprime beam, due to its adjustable focusing ability and controllable orbital angular momentum, has attracted significant attention in fields such as free-space optical communication and particle trapping. However, systematic studies on the propagation behavior of oscillating solitons in PT-symmetric optical lattices remain scarce, particularly regarding their formation mechanisms and self-accelerating characteristics. In this study, the propagation characteristics of Airyprime beams in PT symmetric optical lattices are numerically studied using the split-step Fourier method, and the generation mechanism and control factors of oscillating solitons are analyzed. The influence of lattice parameters (such as the modulation depth P, modulation frequency w, and gain/loss distribution coefficient W₀) and beam initial characteristics (such as the truncation coefficient a) on the dynamic behavior of the beam is revealed. The results show that the initial parameters determine the propagation characteristics of the beam and the stability of the soliton. This research provides theoretical support for beam shaping, optical path design, and nonlinear optical manipulation and has important application value.

In recent years, Airyprime pulses have attracted much attention in the field of nonlinear optics due to their diffraction-free, self-accelerating, and self-healing properties, as well as their unique oscillating tail structure. However, Airyprime pulses are affected by higher-order dispersion and Raman effect in the relaxation nonlinear medium, and their propagation properties have not been thoroughly studied. To this end, the propagation properties of Airyprime pulses in relaxing nonlinear media are systematically investigated in this article by using the stepwise Fourier algorithm. The results show that the propagation behavior of the pulse is affected by multiple factors such as dispersion, self-phase modulation, and Raman effect, among which the third-order dispersion and Raman effect play a key role in the propagation characteristics. By adjusting the parameters of the medium and the pulse’s initial conditions, the pulse’s time-domain propagation trajectory and spectral characteristics can be effectively controlled. These research results provide theoretical support for nonlinear optical applications and important guidance for the design of distributed fiber-optic sensing systems in geophysics, showing a broad application prospect.