Gauge Equivalence, Supersymmetry and Classical Solutions of the ospu($1,1\mathrm{/}1$) Heisenberg Model and the Nonlinear Schr\"odinger Equation

An integrable generalization of the continuous classical O$(2,1)$ pseudospin Heisenberg model to the case of the ospu$(1,1\mathrm{/}1)$ superalgebra is constructed. The gauge equivalence of the constructed model and the related NLSE is established. We indicate a method of generating classical solutions using the global ospu$(1,1\mathrm{/}1)$ supersymmetry. The relationship between solutions of O$(2,1)$ HM and ‘superpartners’ of NLSE is obtained.