Fractional-order effects on the dynamics and lifetime of ring dark solitons in spin–orbit coupled spin-1 Bose–Einstein condensate

This paper investigates the impact of fractional-order effects on the evolution behavior of post-collapse vortices and the lifetime of ring dark solitons (RDSs) in spin–orbit coupled (SOC) spin-1 Bose–Einstein condensate. The numerical results demonstrate that the existence of SOC decreases the lifetime of RDS governed by the equation compared with the three-component RDS without SOC. At the same time, the shallow RDS of the fractional-order system central vortex collapses and gradually disappears without generating any new vortices. On the other hand, deep RDS exhibits a varying number of vortex pairs as the Lévy index decreases, and these remaining vortex pairs undergo complex dynamic evolution over time. RDSs can maintain stable transmission over long distances, but when RDS with vortices is affected by white noise, the time of ring break will be advanced. Regardless of whether it is deep or shallow RDS, a smaller Lévy index corresponds to a shorter RDS lifetime.