On a integrable deformations of Heisenberg supermagnetic model

The Heisenberg supermagnet model which is the supersymmetric generalization of the Heisenberg ferro-magnet 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.