###### Abstract  
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 \(W_{0}\)) 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  
basis for the precise tuning of the focal length of self-focusing beams [7]. In addition, in chiral media, circular Airyprime beams exhibit unique autofocusing properties, and the focal distance and peak intensity of their left and right rotationally polarized components can be flexibly adjusted [8]. In 2024, [PERSON] et al. posited for the first time that circular Airyprime beams exhibit periodic evolutionary behavior in a parabolic potential medium and found that the focal distance of circular Airyprime beams is significantly affected by the parameters of their parabolic potential [9]. It was also found that the focal distance was significantly affected by the parameters of the parabolic potential. Based on Fourier spatial modulation technology, [PERSON]'s team realized the adjustable self-focusing characteristics of circular Airyprime beams [10]. These research results provide new methods and ideas for the application of Airyprime beams in the fields of particle trapping and free-space optical communication. At the same time, the concept of PT symmetric medium has attracted widespread attention in the field of optics and quantum mechanics. Previous studies have focused on constructing PT symmetric optical potential and exploring its basic properties. For example, the tunable PT symmetric optical potential constructed by a coherent four-level atomic medium opens up a new way to further explore related physical phenomena [11]. The study of the kink spectrum shows that the relative position of the kink center and the PT symmetry center will significantly affect the stability of the kink spectrum [12]. Under the action of PT symmetric potential, [PERSON] et al. found that the stability of the local solution of the power-law nonlinear Schrodinger equation is closely related to the imaginary part of the potential and the self-focusing characteristics of the medium [13]. At the same time, an anti-PT symmetric optical coupler was also proposed, and it was shown that it operates in the PT conjugate mode under Kerr nonlinearity [14]. With the deepening of research, people have begun to pay attention to the nonlinear effects, pulse propagation characteristics, and application in complex structures of PT symmetric media. For example, the application of the effective medium theory to PT symmetric multi-layer systems is discussed in depth, and the limitations of the traditional theory are clarified [15]; the phenomena of thresholdless PT symmetry breaking and unidirectional scattering [16] have been successfully realized. In Bragg geometry, the propagation of long and short pulses in quasi-PT symmetric media shows significant differences, indicating the influence of the pulse width on PT symmetric propagation [17]. [PERSON] et al. found that the Bragg diffraction of chirped pulses can exhibit unique phenomena in dispersive quasi-PT symmetric photonic crystals [18]. At present, the research has begun to pay attention to the influence of the PT symmetric lattice on beam transmission characteristics.