Abstract:
In this paper, we consider the dynamics of two interacting point vortex rings in
a Bose – Einstein condensate. The existence of an invariant manifold corresponding to vortex
rings is proved. Equations of motion on this invariant manifold are obtained for an arbitrary
number of rings from an arbitrary number of vortices. A detailed analysis is made of the case
of two vortex rings each of which consists of two point vortices where all vortices have same
topological charge. For this case, partial solutions are found and a complete bifurcation analysis
is carried out. It is shown that, depending on the parameters of the Bose – Einstein condensate,
there are three different types of bifurcation diagrams. For each type, typical phase portraits
are presented.
Keywords:
Bose – Einstein condensate, point vortices, vortex rings, bifurcation analysis.
The work of A. A. Kilin (Sections 1–5) was performed at the Ural Mathematical Center
(Agreement No. 075-02-2022-889). This work of E. M. Artemova (Section 6) was supported by the
framework of the state assignment or the Ministry of Science and Higher Education (No. FEWS-
2020-0009) and was supported in part by the Moebius Contest Foundation for Young Scientists.
Citation:
Elizaveta M. Artemova, Alexander A. Kilin, “Dynamics of Two Vortex Rings in a Bose – Einstein Condensate”, Regul. Chaotic Dyn., 27:6 (2022), 713–732
\Bibitem{ArtKil22}
\by Elizaveta M. Artemova, Alexander A. Kilin
\paper Dynamics of Two Vortex Rings in a Bose – Einstein Condensate
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 6
\pages 713--732
\mathnet{http://mi.mathnet.ru/rcd1189}
\crossref{https://doi.org/10.1134/S1560354722060089}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4519675}
Linking options:
https://www.mathnet.ru/eng/rcd1189
https://www.mathnet.ru/eng/rcd/v27/i6/p713
This publication is cited in the following 3 articles:
Elizaveta Artemova, Evgeny Vetchanin, “The motion of a circular foil in the field of a fixed point singularity: Integrability and asymptotic behavior”, Physics of Fluids, 36:2 (2024)
Victor V. Kuzenov, Sergei V. Ryzhkov, Aleksey Yu Varaksin, “Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme”, Journal of Computational and Applied Mathematics, 451 (2024), 116098
Alexander A. Kilin, Anna M. Gavrilova, Elizaveta M. Artemova, “Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case”, Regul. Chaot. Dyn., 2024
Citation in format AMSBIB
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