Abstract
Abstract This paper is concerned with the construction of two types of generalized Heisenberg supermagnetic models with the constraint S^3=S, including inhomogeneous Heisenberg supermagnet model in (1+1)-dimensional and the $(2+1)$-dimensional Heisenberg supermagnet model. Furthermore, by means of the gauge transformation, we investigate the gauge equivalent counterparts, which are (1+1)-dimensional inhomogeneous nonlinear Schr"odinger equation and (2+1)-dimensional super nonlinear Schr"odinger equation, respectively.
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