Prolongation structures for supersymmetric equations

The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of the resulting Lie superalgebra is determined. It is shown to be isomorphic to RMR*Cov+(C(2), sigma ), where RMR is an eight-dimensional radical. An auto-Backlund transformation is derived from the prolongation structure and the relationship with known solution methods of the SKdV equation is analysed. In addition it is indicated how a super-position principle for the SKdV equation can be obtained