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

This article is cited in 10 scientific papers (total in 10 papers)

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 systems 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.


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Document Type: Article
MSC: 37N05, 76M23
Received: 14.08.2014
Language: English

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
\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

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    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  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    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  mathnet  crossref  mathscinet
    4. Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366  mathnet  crossref  mathscinet
    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  mathnet  crossref  mathscinet
    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  mathnet  crossref
    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  mathnet  crossref
    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  mathnet  crossref
    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  mathnet  crossref  mathscinet  adsnasa
    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  mathnet  crossref
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