Geodesic
Stability of regular vortex polygons in Bose--Einstein condensate
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 56 (2020), pp. 20-29

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We consider the problem of the stability of rotating regular vortex $N$-gons (Thomson configurations) in a Bose–Einstein condensate in a harmonic trap. The dependence of the rotation velocity $\omega$ of the Thomson configuration around the center of the trap is obtained as a function of the number of vortices $N$ and the radius of the configuration $ R $. The analysis of the stability of motion of such configurations in the linear approximation is carried out. For $N \leqslant 6$, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex $N$-gons for $N > 6$ are unstable for any parameters of the system.
Keywords: vortex dynamics, Bose–Einstein condensate, linear stability.
Mots-clés : Thomson configurations 
@article{IIMI_2020_56_a2,
     author = {A. A. Kilin and E. M. Artemova},
     title = {Stability of regular vortex polygons in {Bose--Einstein} condensate},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {20--29},
     publisher = {mathdoc},
     volume = {56},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2020_56_a2/}
}
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A. A. Kilin; E. M. Artemova. Stability of regular vortex polygons in Bose--Einstein condensate. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 56 (2020), pp. 20-29. http://geodesic.mathdoc.fr/item/IIMI_2020_56_a2/