Abstract
The Heisenberg supermagnet model is a supersymmetric system and has a close relationship with the strong electron-correlated Hubbard model. In this paper, the supersymmetric prolongation structure is used to analyze the high order supersymmetric nonlinear equation. The Lax representation is constructed for the prolongation algebra of this equation. The Bäcklund transformation of the supersymmetric nonlinear Schrödinger equation is obtained by simplified calculation.
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