Novel solvable many-body problems

2016/01/19 by Oksana Bihun, F. Calogero, Bihun, Oksana +1
Mathematics · Physics and Astronomy · #12D99 #70F10 #70K42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1601.04793

openalex publication_date 2016/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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