On a integrable deformations of Heisenberg supermagnetic model

The Heisenberg supermagnet model which is the supersymmetric generalization of the Heisenberg ferromagnet model is an important integrable system. We consider the deformations of Heisenberg supermagnet model under the two constraint 1. S² = S for S ∈ USPL(2/1)/S(L(1/1) × U(1)) and 2. S² = 3S ? 2I S ∈ USPL(2/1)/S(U(2) × U(1)). By means of the gauge transformation, we construct the gauge equivalent counterparts, i.e., the super generalized Hirota equation and Gramman odd nonlinear Schrödinger equation.