arXiv:solv-int/9811016

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 system with interesting
integrability properties. We demonstrate the Painlevé property
for some simple but nontrivial reductions of this system, and also
discuss peakon-type solutions.