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Quantum resolution of the nonlinear super-Schrödinger equation. (English) Zbl 1080.81017

Summary: We introduce a \(\mathbb Z_{2}\)-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.

MSC:

81R12 Groups and algebras in quantum theory and relations with integrable systems
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q60 Supersymmetry and quantum mechanics
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