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arXiv · 1407.1641

Multi-particle dynamical systems and polynomials

Maria V. Demina·Nikolai A. Kudryashov
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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 a partial differential equations is described. 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. Our approach is also applicable to dynamical systems that are not multi--particle by their nature but that can be regarded as multi--particle (for example, the Darboux--Halphen system and its generalizations). A wide class of two and three--particle polynomial dynamical systems is integrated.

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Maria V. Demina, Nikolai A. Kudryashov. 2014-07-07. Multi-particle dynamical systems and polynomials. https://arxiv.org/abs/1407.1641

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