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Nelin. Dinam., 2019, Volume 15, Number 1, Pages 59–66 (Mi nd640)  

Nonlinear physics and mechanics

Phase Topology of Two Vortices of Identical Intensities in a Bose Einstein Condensate

P. E. Ryabovabc, S. V. Sokolovdb

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

Abstract: A completely Liouville integrable Hamiltonian system with two degrees of freedom describing the dynamics of two vortex filaments in a Bose Einstein condensate enclosed in a cylindrical trap is considered. For the system of two vortices with identical intensities a bifurcation of three Liouville tori into one is detected. Such a bifurcation is found in the integrable case of Goryachev Chaplygin Sretensky in rigid body dynamics.

Keywords: Vortex dynamics, Bose Einstein condensate, completely integrable Hamiltonian systems, bifurcation diagram of momentum mapping, bifurcations of Liouville tori

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
1.2404.2017/4.6
Russian Foundation for Basic Research 16-01-00809
18-01-00335
18-29-10051
16-01-00170
17-01-00846
The work of S.V. Sokolov (Sections 1, 2) was carried out at MIPT under project 5100 for state support for leading universities of the Russian Federation and also partially support by RFBR grants 16-01-00809, 18-01-00335 and 18-29-10051. The work of P.E.Ryabov (Sections 3, 4) was supported by RFBR grants 16-01-00170 and 17-01-00846 and was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2404.2017/4.6).


DOI: https://doi.org/10.20537/nd190106

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Document Type: Article
MSC: 76M23, 37J35, 37J05, 34A05
Received: 31.12.2018
Accepted:13.02.2019
Language: English

Citation: P. E. Ryabov, S. V. Sokolov, “Phase Topology of Two Vortices of Identical Intensities in a Bose Einstein Condensate”, Nelin. Dinam., 15:1 (2019), 59–66

Citation in format AMSBIB
\Bibitem{RyaSok19}
\by P. E. Ryabov, S. V. Sokolov
\paper Phase Topology of Two Vortices of Identical Intensities in a Bose Einstein Condensate
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 1
\pages 59--66
\mathnet{http://mi.mathnet.ru/nd640}
\crossref{https://doi.org/10.20537/nd190106}


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