Prolongation structure and inverse scattering formalism for the supersymmetric Sine-Gordon equation in ordinary space-time variables

The differential geometric formalism of Whalquist and Estabrook is used to deduce the inverse scattering equations for the supersymmetric Sine-Gordon equation in ordinary space-time variables. The authors deliberately avoid the use of an anticommuting co-ordinate theta, so that the usual quantum mechanical scattering analysis can be performed, the results agree with those of Girrardello et al. when their ansatz is expanded in theta. (Auth.)