A Super-Integrable Discretization of the Calogero Model

Details A Super-Integrable Discretization of the Calogero Model A Super-Integrable Discretization of the Calogero Model

2004-09-16

arxiv.org/abs/nlin/0409031v2

J.Math.Phys. 46 (2005) 062705

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, 5 figures. Added references. Corrected typos

Scientific paper

10.1063/1.1931043

A time-discretization that preserves the super-integrability of the Calogero model is obtained by application of the integrable time-discretization of the harmonic oscillator to the projection method for the Calogero model with continuous time. In particular, the difference equations of motion, which provide an explicit scheme for time-integration, are explicitly presented for the two-body case. Numerical results exhibit that the scheme conserves all the$(=3)$ conserved quantities of the (two-body) Calogero model with a precision of the machine epsilon times the number of iterations.

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