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 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

 Regul. Chaotic Dyn., 2014, Volume 19, Issue 6, Pages 694–701 (Mi rcd192)

The Dynamics of Three Vortex Sources

Ivan A. Bizyaeva, Alexey V. Borisovba, Ivan S. Mamaevca

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
c Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudnyi, 141700 Russia

Abstract: In this paper, the integrability of the equations of a system of three vortex sources is shown. A reduced system describing, up to similarity, the evolution of the system’s configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.

Keywords: integrability, vortex sources, shape sphere, reduction, homothetic configurations

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation Russian Foundation for Basic Research 14-01-00395-a The work of I. S. Mamaev and I. A. Bizyaev was supported by the Ministry of Education and Science of the Russian Federation within the framework of the basic part of the state assignment to institutions of higher education. The work of A. V. Borisov was supported by the RFBR Grant 14-01-00395-a.

DOI: https://doi.org/10.1134/S1560354714060070

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Bibliographic databases:

MSC: 37N05, 76M23
Accepted:08.09.2014
Language:

Citation: Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Three Vortex Sources”, Regul. Chaotic Dyn., 19:6 (2014), 694–701

Citation in format AMSBIB
\Bibitem{BizBorMam14} \by Ivan~A.~Bizyaev, Alexey~V.~Borisov, Ivan~S.~Mamaev \paper The Dynamics of Three Vortex Sources \jour Regul. Chaotic Dyn. \yr 2014 \vol 19 \issue 6 \pages 694--701 \mathnet{http://mi.mathnet.ru/rcd192} \crossref{https://doi.org/10.1134/S1560354714060070} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3284609} \zmath{https://zbmath.org/?q=an:06507827} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000345996200007} 

• http://mi.mathnet.ru/eng/rcd192
• http://mi.mathnet.ru/eng/rcd/v19/i6/p694

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. V. Sokolov, “On the problem of falling motion of a circular cylinder and a vortex pair in a perfect fluid”, Dokl. Math., 94:2 (2016), 594–597
2. Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions”, Regul. Chaotic Dyn., 20:4 (2015), 486–496
3. Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
4. Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366
5. 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
6. N. A. Kudryashov, D. I. Sinelshchikov, “On the Integrability Conditions for a Family of Liénard-type Equations”, Regul. Chaotic Dyn., 21:5 (2016), 548–555
7. 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
8. 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
9. Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov, “Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall”, Regul. Chaotic Dyn., 23:3 (2018), 257–272
10. 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