Abstract:
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi-particle dynamical system by finding polynomial solutions of partial differential equations is introduced. The method enables one to integrate a wide class of polynomial multi-particle dynamical systems. The general solutions of certain dynamical systems related to linear second-order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived.
This research was partially supported by the Russian Science Foundation, project to support research carried out by individual research groups No. 14-11-00258.
\Bibitem{DemKud16}
\by Maria V. Demina, Nikolai A. Kudryashov
\paper Multi-particle Dynamical Systems and Polynomials
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 3
\pages 351--366
\mathnet{http://mi.mathnet.ru/rcd82}
\crossref{https://doi.org/10.1134/S1560354716030072}
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This publication is cited in the following 6 articles:
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
Sarbarish Chakravarty, Michael Zowada, “Classification of KPI lumps”, J. Phys. A: Math. Theor., 55:21 (2022), 215701
Y. Liu, J. Wei, “Multivortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials”, SIAM J. Math. Anal., 52:4 (2020), 3546–3579
D. Gomez-Ullate, Y. Grandati, R. Milson, “Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials”, Stud. Appl. Math., 141:4, SI (2018), 596–625
M. V. Demina, N. A. Kudryashov, J. E. Semenova, “Point vortices in the plane: positive-dimensional configurations”, VI International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012009
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