Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces

Symmetry Integrability and Geometry-Methods and Applications

article

Oksana Bihun¹  Francesco Calogero² 

[1] Department of Mathematics, Concordia College at Moorhead;Physics Department, University of Rome ''La Sapienza'', Istituto Nazionale di Fisica Nucleare

关键词: many-body problems;    N-body problems;    partial dif ferential equations;    isochronous systems;   

DOI  :  10.3842/SIGMA.2013.059

来源: National Academy of Science of Ukraine

【 摘 要 】

The class of solvable many-body problems ''of goldfish type'' is extended by including (the additional presence of) three-body forces. The solvable N -body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary ''coupling constants''. Restrictions on these constants are identified which cause these systems – or appropriate variants of them – to be isochronous or asymptotically isochronous , i.e. all their solutions to be periodic with a fixed period (independent of the initial data) or to have this property up to contributions vanishing exponentially as t → ∞.

【 授权许可】

Unknown