The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group
Chandrashekar Devchand and Jeremy Schiff
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Submission date: 23. Jan. 1999
published in: Journal of mathematical physics, 42 (2001) 1, p. 260-273
DOI number (of the published article): 10.1063/1.1330196
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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 H1 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 Painlevé property for some simple but nontrivial reductions of this system.