We present Backlund transformations (BTs) With parameter for certain classical integrable n-body systems, namely the many-body generalized 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.
Hone, A., Kuznetsov, V.b., Ragnisco, O. (1999). Backlund transformations for many-body systems related to KdV. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 32(27), L299-L306 [10.1088/0305-4470/32/27/102].
Backlund transformations for many-body systems related to KdV
RAGNISCO, Orlando
1999-01-01
Abstract
We present Backlund transformations (BTs) With parameter for certain classical integrable n-body systems, namely the many-body generalized 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
