The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group

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 Painlevé property for some simple but nontrivial reductions of this system.

14 pages, latex file

References in corpus (7)

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• Geodesic Flow and Two (Super) Component Analog of the Camassa-Holm Equation
• Euler Equations Related to the Generalized Neveu-Schwarz Algebra
• A bi-Hamiltonian supersymmetric geodesic equation
• Supersymmetric integrable systems from geodesic flows on superconformal groups