Multi-particle dynamical systems and polynomials
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.
Cite
@article{arxiv.1407.1641,
title = {Multi-particle dynamical systems and polynomials},
author = {Maria V. Demina and Nikolai A. Kudryashov},
journal= {arXiv preprint arXiv:1407.1641},
year = {2014}
}