Two-dimensional vortex dipole, tripole, and quadrupole solitons in nonlocal nonlinearity with Gaussian potential well and barrier.

In this work, we investigate the dynamics and stability of two-dimensional (2D) vortex dipole, tripole, and quadrupole solitons with fundamental topological charge (m = 1) and higher topological charge (m > 1) in nonlocal nonlinearity with Gaussian potential well and barrier. Both analytical and numerical methods are applied to explore these vortex solitons. The analytical expressions are derived by utilizing the variational approach. The numerical simulations show that nonlocality cannot stabilize the vortex dipole, tripole, and quadrupole beams with topological charge m = 1. Interestingly, it is found that these vortex solitons remain stable during propagation only when the topological charge is m = 2 and when the propagation constants are below specific thresholds, where the vortex beams can maintain their profile no matter whether the nonlocality is weak, intermediate, or strong or how the Gaussian potential barrier height (well depth) increases. Furthermore, for the solitons with higher topological charge (m = 4), another consistent pattern emerges, that is, vortex dipole, tripole, and quadrupole solitons split into stable petal solitons and fundamental solitons with the number of petal solitons corresponding to the number of vortex solitons present. The analytical results are verified by numerical simulations.