This article is cited in 5 scientific papers (total in 5 papers)
The Dynamics of Vortex Sources in a Deformation Flow
Ivan A. Bizyaeva, Alexey V. Borisova, Ivan S. Mamaevab
a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia
This paper is concerned with the dynamics of vortex sources in a deformation flow. The case of two vortex sources is shown to be integrable by quadratures. In addition, the relative equilibria (of the reduced system) are examined in detail and it is shown that in this case the trajectory of vortex sources is an ellipse.
integrability, vortex sources, reduction, deformation flow
|Russian Science Foundation
|Russian Foundation for Basic Research
|The work of I. A. Bizyaev (Section 3) was carried out within the framework of the state assignment for institutions of higher education and partially supported by the Dynasty Foundation. The work of A. V. Borisov (Sections 1, 2) was supported by the Russian Science Foundation (project No. 15-12-20035). The work of I. S. Mamaev (Sections 4, 5) was supported by the RFBR grants Nos. 14-01-00395-a and 15-38-20879 mol_a_ved.
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Vortex Sources in a Deformation Flow”, Regul. Chaotic Dyn., 21:3 (2016), 367–376
Citation in format AMSBIB
\by Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
\paper The Dynamics of Vortex Sources in a Deformation Flow
\jour Regul. Chaotic Dyn.
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Evgeny V. Vetchanin, Ivan S. Mamaev, “Dynamics of Two Point Vortices in an External Compressible Shear Flow”, Regul. Chaotic Dyn., 22:8 (2017), 893–908
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
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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
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