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 Regul. Chaotic Dyn., 2017, Volume 22, Issue 8, Pages 976–995 (Mi rcd303)

Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs

Sergei V. Sokolovab, Pavel E. Ryabovacd

a Institute of Machines Science, Russian Academy of Sciences, Maly Kharitonyevsky per. 4, Moscow, 101990 Russia
b Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudny, Moscow Region, 141701 Russia
c Financial University under the Government of the Russian Federation, Leningradsky prosp. 49, Moscow, 125993 Russia
d Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: This paper is concerned with a system two point vortices in a Bose–Einstein condensate enclosed in a trap. The Hamiltonian form of equations of motion is presented and its Liouville integrability is shown. A bifurcation diagram is constructed, analysis of bifurcations of Liouville tori is carried out for the case of opposite-signed vortices, and the types of critical motions are identified.

Keywords: integrable Hamiltonian systems, Bose – Einstein condensate, point vortices, bifurcation analysis

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation Russian Foundation for Basic Research 16-01-0080916-01-0017017-01-00846-a The work of S.V. Sokolov (Sections 1–6) was carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation and also partially support by RFBR grants 16-01-00809. The work of P.E.Ryabov (Sections 4–6) was supported by RFBR grants 16-01-00170 and 17-01-00846-a.

DOI: https://doi.org/10.1134/S1560354717080068

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Bibliographic databases:

Document Type: Article
MSC: 70E05, 70E17, 37J35, 34A05
Accepted:27.11.2017
Language: English

Citation: Sergei V. Sokolov, Pavel E. Ryabov, “Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs”, Regul. Chaotic Dyn., 22:8 (2017), 976–995

Citation in format AMSBIB
\Bibitem{SokRya17} \by Sergei V. Sokolov, Pavel E. Ryabov \paper Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs \jour Regul. Chaotic Dyn. \yr 2017 \vol 22 \issue 8 \pages 976--995 \mathnet{http://mi.mathnet.ru/rcd303} \crossref{https://doi.org/10.1134/S1560354717080068} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425981500006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042431088} 

• http://mi.mathnet.ru/eng/rcd303
• http://mi.mathnet.ru/eng/rcd/v22/i8/p976

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Sokolov S.V. Ryabov P.E., “Bifurcation Diagram of the Two Vortices in a Bose–Einstein Condensate With Intensities of the Same Signs”, Dokl. Math., 97:3 (2018), 286–290
2. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636