A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants. Issue 2 (2nd April 2016)

• Record Type: Journal Article
• Authors: Calogero, Francesco
• Is Part Of: Journal of nonlinear mathematical physics. Volume 23:Issue 2(2016)
• Page Start: 300
• Page End: 305
• Publication Date: 2016-04-02
• Subjects: Solvable N-body problems -- integrable N-body problems -- integrable dynamical systems; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2016.1175823
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract: A N -body problem "of goldfish type" is introduced, the Newtonian ("acceleration equal force") equations of motion of which describe the motion of N pointlike unit-mass particles moving in the complex z -plane. The model—for arbitrary N —is solvable, namely its configuration (positions and velocities of the N "particles") at any later time t can be obtained from its configuration at the initial time by algebraic operations. It features specific nonlinear velocity-dependent many-body forces depending on N 2 arbitrary (complex) coupling constants. Sufficient conditions on these constants are identified which cause the model to be isochronous—so that all its solutions are then periodic with a fixed period independent of the initial data. A variant with twice as many arbitrary coupling constants, or even more, is also identified.