Abstract
We introduce a ℤ2-graded version of the nonlinear Schrödinger 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.
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