Backlund transformations for many-body systems related to KdV

Details Backlund transformations for many-body systems related to KdV Backlund transformations for many-body systems related to KdV

1999-03-29

arxiv.org/abs/solv-int/9904003v1

J.Phys. A32 (1999) L299-L306

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 8 pages

Scientific paper

10.1088/0305-4470/32/27/102

We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these systems may be obtained as particular reductions (stationary or restricted flows) of the KdV hierarchy; alternatively they may be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide exact time-discretizations of the original (continuous) systems, preserving the Lax matrix and hence all integrals of motion, and satisfy the spectrality property with respect to the Backlund parameter.

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