(2+1)-Dimensional Generalized Third-Order Heisenberg Supermagnet Model

The Heisenberg supermagnet model is an important supersymmetric integrable system which is the super extension of the Heisenberg ferromagnet model. By virtue of introducing the general auxiliary matrix variables, we construct a new (2 + 1)-dimensional generalized integrable Heisenberg supermagnet models under two constraints. Meanwhile, we establish their corresponding gauge equivalent counterparts. Moreover, we derive new solutions of the supersymmetric integrable systems by means of the Backlund transformations.