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

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

1998-11-22

arxiv.org/abs/solv-int/9811016v1

J.Math.Phys. 42 (2001) 260-273

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, latex file

Scientific paper

10.1063/1.1330196

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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