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Dynamics of Two Vortex Rings in a Bose – Einstein Condensate

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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.

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Funding

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.

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Authors and Affiliations

  1. Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, 426034, Izhevsk, Russia

    Elizaveta M. Artemova & Alexander A. Kilin

  2. Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, 620990, Ekaterinburg, Russia

    Alexander A. Kilin

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  1. Elizaveta M. Artemova
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Correspondence to Elizaveta M. Artemova or Alexander A. Kilin.

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76B47, 37J20, 34C23, 34C45

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Artemova, E.M., Kilin, A.A. Dynamics of Two Vortex Rings in a Bose – Einstein Condensate. Regul. Chaot. Dyn. 27, 713–732 (2022). https://doi.org/10.1134/S1560354722060089

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