dorsal/arxiv
View SchemaThe supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group
| Authors | Chandrashekar Devchand, Jeremy Schiff |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9811016 |
| URL | https://arxiv.org/abs/solv-int/9811016 |
| DOI | 10.1063/1.1330196 |
| Journal | J.Math.Phys. 42 (2001) 260-273 |
Abstract
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the group of superconformal transformations in two dimensions, (b) equations which are hamiltonian with respect to a different hamiltonian structure and (c) supersymmetric flow equations. Classes (a) and (b) have no intersection, but the intersection of classes (a) and (c) gives a candidate for a new supersymmetric integrable system. We demonstrate the Painlev\'e property for some simple but nontrivial reductions of this system.
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"abstract": "We study a family of fermionic extensions of the Camassa-Holm equation.\nWithin this family we identify three interesting classes: (a) equations, which\nare inherently hamiltonian, describing geodesic flow with respect to an H^1\nmetric on the group of superconformal transformations in two dimensions, (b)\nequations which are hamiltonian with respect to a different hamiltonian\nstructure and (c) supersymmetric flow equations. Classes (a) and (b) have no\nintersection, but the intersection of classes (a) and (c) gives a candidate for\na new supersymmetric integrable system. We demonstrate the Painlev\\\u0027e property\nfor some simple but nontrivial reductions of this system.",
"arxiv_id": "solv-int/9811016",
"authors": [
"Chandrashekar Devchand",
"Jeremy Schiff"
],
"categories": [
"solv-int",
"hep-th",
"math-ph",
"math.DG",
"math.MP",
"nlin.SI"
],
"doi": "10.1063/1.1330196",
"journal_ref": "J.Math.Phys. 42 (2001) 260-273",
"title": "The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group",
"url": "https://arxiv.org/abs/solv-int/9811016"
},
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