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Backlund transformations for many-body systems related to KdV

A. N. W. Hone·V. B. Kuznetsov·O. Ragnisco
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Abstract

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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BibTeXRIS

A. N. W. Hone, V. B. Kuznetsov, O. Ragnisco. 1999-03-29. Backlund transformations for many-body systems related to KdV. https://doi.org/10.1088/0305-4470%2F32%2F27%2F102

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