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Regular version of the site

Article

Multi-particle Dynamical Systems and Polynomials

Regular and Chaotic Dynamics. 2016. Vol. 21. No. 3. P. 351-366.
Demina M.V., Kudryashov N. A.

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.