On the higher order Heisenberg supermagnet model in (2+1)-dimensions

In this paper we construct the higher order Heisenberg supermagnet models in (2+1)-dimensions by introducing different auxiliary matrix variables. We investigate their structure and integrability with respect to two constraints. By virtue of the gauge transformation, we derive their gauge equivalent counterparts which are the super and fermionic higher order nonlinear Schrödinger equations in (2+1)-dimensions. Furthermore, we obtain their corresponding Bäcklund transformations.