Novel solvable many-body problems

TL;DR

This paper introduces new solvable many-body dynamical systems with complex-plane points, characterized by nonlinear Newtonian equations, which can be solved algebraically and exhibit diverse behaviors like periodicity and scattering.

Contribution

It presents novel classes of solvable many-body problems with nonlinear equations of motion in the complex plane, expanding the scope of integrable dynamical systems.

Findings

Models are solvable via algebraic operations

Some models are multiply periodic or isochronous

Others exhibit scattering phenomena

Abstract

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These models are solvable, namely their configuration at any time can be obtained from the initial data by algebraic operations, amounting to the determination of the zeros of a known time-dependent polynomial in the independent variable z. Some of these models are multiply periodic, isochronous or asymptotically isochronous; others display scattering phenomena.