  In this paper we construct the two component supersymmetric generalized Harry
Dym equation which is integrable and study various properties of this model in
the bosonic limit. In particular, in the bosonic limit we obtain a new
integrable system which, under a hodograph transformation, reduces to a coupled
three component system. We show how the Hamiltonian structure transforms under
a hodograph transformation and study the properties of the model under a
further reduction to a two component system. We find a third Hamiltonian
structure for this system (which has been shown earlier to be a bi-Hamiltonian
system) making this a genuinely tri-Hamiltonian system. The connection of this
system to the modified dispersive water wave equation is clarified. We also
study various properties in the dispersionless limit of our model.
