We theoretically investigate the stable mechanism of a ring soliton in two-dimensional Fermi superfluids by solving the Bogoliubov–de Gennes equations and their time-dependent counterparts. In the uniform situation, we discover that the ring soliton is always driven away from its initial location and moves towards the boundary due to a curvature-induced effective potential. The ring soliton is impossible to remain static at any location in the uniform system. To balance the density difference between the ring soliton's two sides, a harmonic trap is introduced, which can exert an effect to counterbalance the curvature-induced effective potential. This enables the ring dark soliton to become a stable state at a particular equilibrium position $r_s$, where the free energy of the ring dark soliton just reaches the maximum value. Once the ring soliton is slightly deviated from $r_s$, some stable periodic oscillations of the ring soliton around $r_s$ will occur. Some dissipation will occur to the ring soliton once its minimum radius is comparable to the healing length of the soliton's Friedel oscillation. This dissipation will increase the oscillation amplitude and, finally, make the ring soliton decay into sound ripples. Our research lays the groundwork for a more in-depth understanding of the stable mechanism of a ring dark soliton in the future.

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• Cold atoms & matter waves
• Fermi gases