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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 5, Pages 371–384
DOI: https://doi.org/10.1134/S1560354712050012 (Mi rcd409) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Point Vortices and Classical Orthogonal Polynomials

Maria V. Demina, Nikolai A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University “MEPhI”, 31 Kashirskoe Shosse, 115409 Moscow, Russian Federation
Citations (11)
DOI: https://doi.org/10.1134/S1560354712050012
Abstract: Stationary equilibria of point vortices in the plane and on the cylinder in the presence of a background flow are studied. Vortex systems with an arbitrary choice of circulations are considered. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one. It is found that polynomials that are Wronskians of classical orthogonal polynomials solve the latter equation. As a consequence vortex equilibria at a certain choice of background flows can be described with the help of Wronskians of classical orthogonal polynomials.
Keywords: point vortices, special polynomials, classical orthogonal polynomials.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation P1228
This research was partially supported by the Federal Target Programm “Research and Scientific–Pedagogical Personnel of Innovation in the Russian Federation for 2009–2013” (Contract P1228).
Received: 24.04.2012
Accepted: 16.06.2012
Bibliographic databases:
Document Type: Article
MSC: 33D45+76M23
Language: English
Citation: Maria V. Demina, Nikolai A. Kudryashov, “Point Vortices and Classical Orthogonal Polynomials”, Regul. Chaotic Dyn., 17:5 (2012), 371–384
Citation in format AMSBIB
\Bibitem{DemKud12}
\by Maria V. Demina, Nikolai A. Kudryashov
\paper Point Vortices and Classical Orthogonal Polynomials
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 371--384
\mathnet{http://mi.mathnet.ru/rcd409}
\crossref{https://doi.org/10.1134/S1560354712050012}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989511}
\zmath{https://zbmath.org/?q=an:1257.33048}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..371D}
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  • https://www.mathnet.ru/eng/rcd/v17/i5/p371
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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