Dynamics of spatiotemporal optical vortices in nonlinear media with different group velocity dispersion

We systematically investigate the propagation dynamics of the spatiotemporal optical vortex (STOV) in nonlocal nonlinear media with a Gaussian response kernel, revealing distinct regimes under different group-velocity dispersion (GVD) and nonlocal response strengths. Based on the nonlocal nonlinear Schrödinger equation, we develop a numerical framework that combines the Petviashvili fixed-point iteration with the symmetric split-step Fourier method. When GVD is coupling-matched with a nonlocal response, STOV exhibits a stable eigenstate or a periodic breathing behavior, which is difficult to achieve in conventional local media. These results demonstrate that nonlocality is essential for maintaining STOV structural stability and highlight the dependence of the breathing period on the interplay between GVD and nonlocality strength.