# Backlund transformations for many-body systems related to KdV

Hone, Andrew N.W., Kuznetsov, Vadim B., Ragnisco, Orlando (1999) Backlund transformations for many-body systems related to KdV. Journal of Physics A: Mathematical and General, 32 (27). L299-L306. ISSN 0305-4470. (doi:10.1088/0305-4470/32/27/102)

## 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.

Item Type: Article 10.1088/0305-4470/32/27/102 Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equationsQ Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanicsQ Science > QC Physics > QC20 Mathematical Physics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Andrew N W Hone 21 Jun 2014 01:36 UTC 06 Feb 2020 04:09 UTC https://kar.kent.ac.uk/id/eprint/41494 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-9780-7369