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2013
Impact Factor

Pavel Ryabov

Leningradsky prospect, 49, Moscow, 125993
Financial University

Publications:

Ryabov P. E., Shadrin A. A.
Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics
2019, vol. 24, no. 4, pp.  418-431
Abstract
This article is devoted to the results of phase topology research on a generalized mathematical model, which covers such two problems as the dynamics of two point vortices enclosed in a harmonic trap in a Bose – Einstein condensate and the dynamics of two point vortices bounded by a circular region in an ideal fluid. New bifurcation diagrams are obtained and three-into-one and four-into-one tori bifurcations are observed for some values of the physical parameters of the model. The presence of such bifurcations in the integrable model of vortex dynamics with positive intensities indicates a complex transition and a connection between bifurcation diagrams in both limiting cases. In this paper, we analytically derive equations that define the parametric family of bifurcation diagrams of the generalized model, including bifurcation diagrams of the specified limiting cases. The dynamics of the bifurcation diagram in a general case is shown using its implicit parameterization. A stable bifurcation diagram, related to the problem of dynamics of two vortices bounded by a circular region in an ideal fluid, is observed for particular parameters’ values.
Keywords: completely integrable Hamiltonian system, bifurcation diagram, bifurcation of Liouville tori, dynamics of point vortices, Bose – Einstein condensate
Citation: Ryabov P. E., Shadrin A. A.,  Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics, Regular and Chaotic Dynamics, 2019, vol. 24, no. 4, pp. 418-431
DOI:10.1134/S156035471904004X
Sokolov S. V., Ryabov P. E.
Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs
2017, vol. 22, no. 8, pp.  976–995
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
Citation: Sokolov S. V., Ryabov P. E.,  Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs, Regular and Chaotic Dynamics, 2017, vol. 22, no. 8, pp. 976–995
DOI:10.1134/S1560354717080068

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