Phase Topology of Two Vortices of Identical Intensities in a Bose – Einstein Condensate
Received 31 December 2018; accepted 13 February 2019
2019, Vol. 15, no. 1, pp. 59-66
Author(s): Ryabov P. E., Sokolov S. V.
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.
Download File PDF, 506 Kb |
References |
|
[1] |
Fetter, A. L., “Rotating Trapped Bose – Einstein Condensates”, Rev. Mod. Phys., 81:2 (2009), |
[2] |
Torres, P. J., Kevrekidis, P. G., Frantzeskakis, D. J., Carretero-González, R., Schmelcher, P., and Hall, D. S., “Dynamics of Vortex Dipoles in Confined Bose – Einstein Condensates”, Phys. Lett. A, 375:33 (2011), |
[3] | Navarro, R., Carretero-González, R., Torres, P. J., Kevrekidis, P. G., Frantzeskakis, D. J., Ray, M. W., Altuntaş, E., and Hall, D. S., “Dynamics of a Few Corotating Vortices in Bose – Einstein Condensates”, Phys. Rev. Lett., 110:22 (2013), 225301, 6 pp. |
[4] | Koukouloyannis, V., Voyatzis, G., and Kevrekidis, P. G., “Dynamics of Three Noncorotating Vortices in Bose – Einstein Condensates”, Phys. Rev. E, 89:4 (2014), 042905, 14 pp. |
[5] |
Borisov, A. V. and Kilin, A. A., “Stability of Thomson's Configurations of Vortices on a Sphere”, Regul. Chaotic Dyn., 5:2 (2000), |
[6] |
Kilin, A. A., Borisov, A. V., and Mamaev, I. S., “The Dynamics of Point Vortices inside and outside a Circular Domain”, Basic and Applied Problems of the Theory of Vortices, eds. A. V. Borisov, I. S. Mamaev, M. A. Sokolovskiy, R&C Dynamics, Institute of Computer Science, Izhevsk, 2003, |
[7] |
Borisov, A. V., Mamaev, I. S., and Kilin, A. A., “Absolute and Relative Choreographies in the Problem of Point Vortices Moving on a Plane”, Regul. Chaotic Dyn., 9:2 (2004), |
[8] |
Borisov, A. V., Kilin, A. A., and Mamaev, I. S., “The Dynamics of Vortex Rings: Leapfrogging, Choreographies and the Stability Problem”, Regul. Chaotic Dyn., 18:1–2 (2013), |
[9] |
Borisov, A. V., Ryabov, P. E., and Sokolov, S. V., “Bifurcation Analysis of a Problem on the Motion of a Cylinder and a Point Vortex in an Ideal Fluid”, Math. Notes, 99:5–6 (2016), |
[10] |
Sokolov, S. V. and Ryabov, P. E., “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), |
[11] |
Sokolov, S. V. and 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), |
[12] | Ryabov, P. E., Bifurcation Diagram of One Perturbed Vortex Dynamics Problem, 2018, arXiv: 1811.10512 [nlin.SI] |
[13] | Ryabov, P. E., On One Unstable Bifurcation in the Dynamics of Vortex Structure, 2018, arXiv: 1812.03563 [nlin.SI] |
[14] | Kharlamov, M. P., Topological Analysis of Integrable Problems of Rigid Body Dynamics, Leningr. Gos. Univ., Leningrad, 1988, 197 pp. (Russian) |
[15] |
Bolsinov, A. V., Matveev, S. V., and Fomenko, A. T., “Topological Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. List of Systems of Small Complexity”, Russian Math. Surveys, 45:2 (1990), |
[16] |
Oshemkov, A. A. and Tuzhilin, M. A., “Integrable Perturbations of Saddle Singularities of Rank |
[17] |
Kharlamov, M. P., “Extensions of the Appelrot Classes for the Generalized Gyrostat in a Double Force Field”, Regul. Chaotic Dyn., 19:2 (2014), |
[18] |
Bolsinov, A. V., Borisov, A. V., and Mamaev, I. S., “Topology and Stability of Integrable Systems”, Russian Math. Surveys, 65:2 (2010), |
[19] |
Ivanov, A. P., “On Singular Points of Equations of Mechanics”, Dokl. Math., 97:2 (2018), |
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License