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.
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.
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
\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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000425981500006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042431088}
Linking options:
https://www.mathnet.ru/eng/rcd303
https://www.mathnet.ru/eng/rcd/v22/i8/p976
This publication is cited in the following 13 articles:
Sergei V. Sokolov, Galina A. Pruss, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING, 3269, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING, 2025, 100001
G. P. Palshin, “Topology of the Liouville foliation in the generalized constrained three-vortex problem”, Sb. Math., 215:5 (2024), 667–702
Sergei V. Sokolov, Pavel E. Ryabov, Sergei M. Ramodanov, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2022, 3030, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2022, 2024, 080001
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)
Gleb Palshin, 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2022, 1
Sergey M. Ramodanov, Sergey V. Sokolov, “Dynamics of a Circular Cylinder and Two Point Vortices
in a Perfect Fluid”, Regul. Chaotic Dyn., 26:6 (2021), 675–691
Gleb P. Palshin, Pavel E. Ryabov, Sergei V. Sokolov, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
P. E. Ryabov, S. V. Sokolov, “Phase Topology of Two Vortices of Identical Intensities in a Bose – Einstein Condensate”, Rus. J. Nonlin. Dyn., 15:1 (2019), 59–66
Pavel E. Ryabov, Artemiy A. Shadrin, “Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics”, Regul. Chaotic Dyn., 24:4 (2019), 418–431
P. E. Ryabov, “Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose–Einstein condensate”, Dokl. Math., 99:2 (2019), 225–229
P. E. Ryabov, “Bifurcation of four liouville tori in one generalized integrable model of vortex dynamics”, Dokl. Phys., 64:8 (2019), 325–329
S. V. Sokolov, P. E. Ryabov, “Bifurcation diagram of the two vortices in a Bose–Einstein condensate with intensities of the same signs”, Dokl. Math., 97:3 (2018), 286–290
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
Citation in format AMSBIB
Contact us: