Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/bifurcation-diagram-of-one-generalized-integrable-model-of-vortex-RONVbX195t
References (27)
-
A. Borisov, A. Kilin, I. Mamaev (2013)
The dynamics of vortex rings: Leapfrogging, choreographies and the stability problemRegular and Chaotic Dynamics, 18
-
P. Ryabov (2019)
Bifurcations of Liouville Tori in a System of Two Vortices of Positive Intensity in a Bose–Einstein CondensateDoklady Mathematics, 99
-
Plane vortex motion // Quart -
S. Sokolov, P. Ryabov (2018)
Bifurcation Diagram of the Two Vortices in a Bose–Einstein Condensate with Intensities of the Same SignsDoklady Mathematics, 97
-
P E Ryabov (2019)
On Bifurcation of the Four Liouville Tori in One Generalized Integrable Model of the Vortex Dynamics -
A. Fetter (2008)
Rotating trapped Bose-Einstein condensatesLaser Physics, 18
-
P. Ryabov, S. Sokolov (2018)
Phase Topology of Two Vortices of the Identical Intensities in Bose-Einstein Condensate.arXiv: Exactly Solvable and Integrable Systems
-
Pedro Torres, P. Kevrekidis, D. Frantzeskakis, R. Carretero-González, P. Schmelcher, Danal Hall (2011)
Dynamics of vortex dipoles in confined BoseEinstein condensatesFuel and Energy Abstracts
-
A. Bolsinov, A. Borisov, I. Mamaev (2010)
Topology and stability of integrable systemsRussian Mathematical Surveys, 65
-
(1988)
Topological Analysis of Integrable Problems of Rigid Body Dynamics -
V. Koukouloyannis, G. Voyatzis, P. Kevrekidis (2013)
Dynamics of three noncorotating vortices in Bose-Einstein condensates.Physical review. E, Statistical, nonlinear, and soft matter physics, 89 4
-
A V Borisov, P E Ryabov, S V Sokolov (2016)
Bifurcation Analysis of a Problem on the Motion of a Cylinder and a Point Vortex in an Ideal FluidMath. Notes, 99
-
A. Bolsinov, S. Matveev, A. Fomenko (1990)
Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexityRussian Mathematical Surveys, 45
-
A. Borisov, A. Kilin (2005)
Stability of Thomson's Configurations of Vortices on a SpherearXiv: Chaotic Dynamics
-
P J Torres, P G Kevrekidis, D J Frantzeskakis, R Carretero-González, P Schmelcher, D S Hall (2011)
Dynamics of Vortex Dipoles in Confined Bose–Einstein CondensatesPhys. Lett. A, 375
-
A G Greenhill (1877)
Plane Vortex MotionQuart. J. Pure Appl. Math., 15
-
M. Kharlamov, P. Ryabov, I. Kharlamova (2017)
Topological Atlas of the Kovalevskaya–Yehia GyrostatJournal of Mathematical Sciences, 227
-
A L Fetter (2009)
Rotating Trapped Bose–Einstein CondensatesRev. Mod. Phys., 81
-
AA Kilin, AV Borisov, IS Mamaev (2005)
Mathematical Methods in the Dynamics of Vortex Structures -
A A Kilin, A V Borisov, I S Mamaev (2003)
Basic and Applied Problems of the Theory of Vortices -
A. Borisov, I. Mamaev, A. Kilin (2005)
ABSOLUTE AND RELATIVE CHOREOGRAPHIES IN THE PROBLEM OF POINT VORTICES MOVING ON A PLANEarXiv: Chaotic Dynamics
-
P. Ryabov (2019)
Bifurcation of Four Liouville Tori in One Generalized Integrable Model of Vortex DynamicsDoklady Physics, 64
-
R. Navarro, R. Carretero-González, P. Torres, P. Kevrekidis, D. Frantzeskakis, M. Ray, Emine Altuntaş, D. Hall (2013)
Dynamics of a few corotating vortices in Bose-Einstein condensates.Physical review letters, 110 22
-
(2003)
The Dynamics of Point Vortices Inside and Outside a Circular Domain, in Basic and Applied Problems of the Theory of Vortices Borisov -
A. Borisov, P. Ryabov, S. Sokolov (2016)
Bifurcation analysis of the motion of a cylinder and a point vortex in an ideal fluidMathematical Notes, 99
-
S. Sokolov, P. Ryabov (2017)
Bifurcation Analysis of the Dynamics of Two Vortices in a Bose–Einstein Condensate. The Case of Intensities of Opposite SignsRegular and Chaotic Dynamics, 22
-
A. Oshemkov, M. Tuzhilin (2018)
Integrable perturbations of saddle singularities of rank 0 of integrable Hamiltonian systemsSbornik: Mathematics, 209
- Publisher
- Springer Journals
- Copyright
- Copyright © 2019 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S156035471904004X
- Publisher site
- See Article on Publisher Site
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.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 6, 2019