Vortex gap solitons in dipolar Bose–Einstein condensates with cubic–quintic nonlinearity and parity-time-symmetric optical lattice

In this study, we explore two-dimensional (2D) vortex solitons (VSs) in dipolar Bose–Einstein condensates with cubic–quintic nonlinearity and a parity-time ($\mathrm{PT}$)-symmetric optical lattice. Using numerical methods, we obtain gap soliton solutions and evaluate their topological and dynamical stability. Two types of VSs, ring-shaped and multicore solitons, are discovered with topological charges ranging from $m=1$ to 3. The behavior and stability of VSs are influenced by key parameters, such as the quintic nonlinearity coefficient, dipole–dipole interaction coefficient, and the imaginary/real parts of the $\mathrm{PT}$-symmetric potential. In particular, the $\mathrm{PT}$-symmetric potential affects the asymmetric distribution of ring-shaped VSs and the topological intensity distribution of multicore VSs. The stability of VSs is evaluated via temporal evolution. These results improve our understanding of soliton dynamics in non-Hermitian systems and offer insights for topological photonic applications.