  The factorisation method commonly used in linear supersymmetric quantum
mechanics is extended, such that it can be applied to nonlinear quantum
mechanical systems. The new method is distinguishable from the linear
formalism, as the superpotential is forced to become eigenfunction-dependent.
An example solution is given for the nonlinear Schroedinger equation and its
supersymmetric partner equation. This method allows new nonlinear evolution
equations to be constructed from the solutions of known nonlinear equations,
and has the potential to be a useful tool for mathematicians and physicists
working in the field of nonlinear systems, allowing the discovery of previously
unknown `dualities' amongst soliton solutions and their respective equations.
