Solitary vortex dynamics of two-dimensional harmonically trapped Bose-Einstein condensates with higher-order nonlinear interactions

We studied the evolutionary patterns of two-dimensional Bose-Einstein condensates incorporating higher-order nonlinear interactions in harmonic potential. Using the Gross-Pitaevskii equation model with higher-order nonlinear corrections, we derived the analytical solitary vortex solutions via the variational method. The impact of the higher-order nonlinear interaction on the vortex dynamics is quantitatively analyzed, showing its key nonlinear feature contribution in the asymmetric vortex evolution with more precise evolutionary pattern generated. We found that, for the circular symmetric solution, if the nonlinear strength is not high, the higher-order nonlinear corrections essentially have only a tiny perturbative effect on the system’s quasi-static oscillation state, whereas for asymmetric evolution of the solitary vortex, incorporating higher-order corrections will generate an evolution pattern that better matches the results of numerical simulation. The theoretical results derived here can be used to guide relevant experimental studies of higher-order nonlinear effects in ultracold atomic systems.