(2+1)-Dimensional Integrable Heisenberg Supermagnet Model

Abstract

The Heisenberg supermagnet models which can be regarded as the superextensions of the Heisenberg ferromagnet model are the important supersymmetric (1+1)-dimensional integrable systems. We investigate their integrability in higher dimensions and construct the (2+1)-dimensional integrable Heisenberg supermagnet models with respect to two different quadratic constraints of the the superspin variable. By means of the gauge transformation, we derive their gauge equivalent counterparts, i.e., the (2+1)-dimensional Grassman odd and super nonlinear Schrodinger equation, respectively.