Open Access
2013 Solvable and/or Integrable Many-Body Models on a Circle
Oksana Bihun, Francesco Calogero
J. Geom. Symmetry Phys. 30: 1-18 (2013). DOI: 10.7546/jgsp-30-2013-1-18


Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion (“accelerations equal forces”) are integrable, i.e., they allow the explicit exhibition of $N$ constants of motion in terms of the dependent variables and their time-derivatives. Some of these models are moreover solvable by purely algebraic operations, by (explicitly performable) quadratures and, finally, by functional inversions. The techniques to manufacture these models are not new; some of these models are themselves new; others are reinterpretations of known models.


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Oksana Bihun. Francesco Calogero. "Solvable and/or Integrable Many-Body Models on a Circle." J. Geom. Symmetry Phys. 30 1 - 18, 2013.


Published: 2013
First available in Project Euclid: 26 May 2017

zbMATH: 1331.70028
MathSciNet: MR3113658
Digital Object Identifier: 10.7546/jgsp-30-2013-1-18

Rights: Copyright © 2013 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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