dorsal/arxiv
View SchemaBacklund transformations for many-body systems related to KdV
| Authors | A. N. W. Hone, V. B. Kuznetsov, O. Ragnisco |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904003 |
| URL | https://arxiv.org/abs/solv-int/9904003 |
| DOI | 10.1088/0305-4470/32/27/102 |
| Journal | J.Phys. A32 (1999) L299-L306 |
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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"abstract": "We present Backlund transformations (BTs) with parameter for certain\nclassical integrable n-body systems, namely the many-body generalised\nHenon-Heiles, Garnier and Neumann systems. Our construction makes use of the\nfact that all these systems may be obtained as particular reductions\n(stationary or restricted flows) of the KdV hierarchy; alternatively they may\nbe considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide\nexact time-discretizations of the original (continuous) systems, preserving the\nLax matrix and hence all integrals of motion, and satisfy the spectrality\nproperty with respect to the Backlund parameter.",
"arxiv_id": "solv-int/9904003",
"authors": [
"A. N. W. Hone",
"V. B. Kuznetsov",
"O. Ragnisco"
],
"categories": [
"solv-int",
"hep-th",
"math-ph",
"math.MP",
"nlin.SI"
],
"doi": "10.1088/0305-4470/32/27/102",
"journal_ref": "J.Phys. A32 (1999) L299-L306",
"title": "Backlund transformations for many-body systems related to KdV",
"url": "https://arxiv.org/abs/solv-int/9904003"
},
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