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Multi-particle dynamical systems and polynomials

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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.

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Authors and Affiliations

  1. National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409, Russia

    Maria V. Demina & Nikolai A. Kudryashov

Authors
  1. Maria V. Demina
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  2. Nikolai A. Kudryashov
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Correspondence to Maria V. Demina.

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To the memory of professors Hassan Aref and Vyacheslav Meleshko

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Demina, M.V., Kudryashov, N.A. Multi-particle dynamical systems and polynomials. Regul. Chaot. Dyn. 21, 351–366 (2016). https://doi.org/10.1134/S1560354716030072

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  • DOI: https://doi.org/10.1134/S1560354716030072

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