Regular and Chaotic Dynamics

, Volume 17, Issue 5, pp 371–384 | Cite as

Point vortices and classical orthogonal polynomials

  • Maria V. Demina
  • Nikolai A. Kudryashov


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.


point vortices special polynomials classical orthogonal polynomials 

MSC2010 numbers



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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Research Nuclear University “MEPhI”MoscowRussian Federation

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