Susy Generalized Harry Dym Equation and Its Bosonic Reduction

Abstract

We construct the two-component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. We obtain in this limit 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.