Abstract
Vortex plays a certain stabilizing role for the ring in the coexistence state of ring dark and anti-dark solitons with vortex due to the interaction between solitons and vortex in Bose-Einstein condensation and nonlinear optics. The numerical results show that the Lévy index for the Fractional-order effect has a great influence on their propagation. When the Lévy index is the optimal value, the ring dark soliton can maintain stable transmission over a longer distance, and the ring anti-dark soliton can also maintain stable transmission over a certain distance.
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