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Description
We investigate the dynamics of topological solitons in two-dimensions (2D) and find that a ring ferrodark soliton (FDS) exhibits self-sustained oscillations in a homogeneous quasi-2D ferromagnetic spin-1 Bose-Einstein condensate (BEC), rather than expected indefinite expansion. Moreover, along with the ring radius oscillation, the nematic tensor at the magnetization-vanishing FDS core also exhibits periodic motion.
When the ring radius greatly exceeds the FDS width, the motion is nearly elastic and we derive the ring-radius equation of motion (EOM) which can be recast into a form analogous to the inviscid Rayleigh-Plesset equation for spherical bubbles in classical fluids, but with anomalous terms.
Exact solutions to this equation, as well as the oscillation frequency and amplitude, are obtained analytically. In the absence of the magnetic field, the ring radius and the non-zero eigenvalue of the nematic tensor at the core, i.e., the mass superfluid density, become stationary, while oscillations of the nematic tensor components, driven by the ring curvature, persist at the core. Excellent agreements are found between analytical predictions and numerical simulations.