  We introduce a Z_2-graded version of the nonlinear Schrodinger equation that
includes one fermion and one boson at the same time. This equation is shown to
possess a supersymmetry which proves to be itself part of a super-Yangian
symmetry based on gl(1|1). The solution exhibits a super version form of the
classical Rosales solution. Then, we second quantize these results, and give a
Lax pair formulation (based on gl(2|1)) for the model.
