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.
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).
\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}
Linking options:
https://www.mathnet.ru/eng/rcd409
https://www.mathnet.ru/eng/rcd/v17/i5/p371
This publication is cited in the following 12 articles:
Pavel Kostenetskiy, Vyacheslav Kozyrev, Roman Chulkevich, Alina Raimova, Communications in Computer and Information Science, 2241, Parallel Computational Technologies, 2024, 49
A. Vishnevskaya, M. V. Demina, “Negative Pell Equation and Stationary Configurations of Point Vortices on the Plane”, Math. Notes, 114:1 (2023), 46–54
Andrei Martínez-Finkelshtein, Ramón Orive, Joaquín Sánchez-Lara, “Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials”, Constr Approx, 58:2 (2023), 271
Kudryashov N.A., “Generalized Hermite Polynomials For the Burgers Hierarchy and Point Vortices”, Chaos Solitons Fractals, 151 (2021), 111256
Dariya V. Safonova, Maria V. Demina, Nikolai A. Kudryashov, “Stationary Configurations of Point Vortices on a Cylinder”, Regul. Chaotic Dyn., 23:5 (2018), 569–579
M V Demina, N A Kudryashov, J E Semenova, “Point vortices in the plane: positive-dimensional configurations”, J. Phys.: Conf. Ser., 937 (2017), 012009
Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366
K V S SHIV CHAITANYA, S SREE RANJANI, PRASANTA K PANIGRAHI, R RADHAKRISHNAN, V SRINIVASAN, “Exceptional polynomials and SUSY quantum mechanics”, Pramana - J Phys, 85:1 (2015), 53
Anna M Barry, F Hajir, P G Kevrekidis, “Generating functions, polynomials and vortices with alternating signs in Bose–Einstein condensates”, J. Phys. A: Math. Theor., 48:15 (2015), 155205
Nikolay A. Kudryashov, “Higher Painlevé Transcendents as Special Solutions of Some Nonlinear Integrable Hierarchies”, Regul. Chaotic Dyn., 19:1 (2014), 48–63
M. V. Demina, N. A. Kudryashov, “Rotation, collapse, and scattering of point vortices”, Theor. Comput. Fluid Dyn., 28:3 (2014), 357
Maria V. Demina, Nikolai A. Kudryashov, “Relative Equilibrium Configurations of Point Vortices on a Sphere”, Regul. Chaotic Dyn., 18:4 (2013), 344–355
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