Supersymmetric integrable systems in \((2+1)\) dimensions and their Bäcklund transformation (Q1805713)

Two approaches to generalize nonlinear integrable systems in \((2+1)\) dimensions which are supersymmetric are proposed. The first one makes use of the homogeneous spaces of super-Lie algebra and the second one extends the dimension of the system. The approach produces two different equations. The Bäcklund transformations of these equations are generated with the help of gauge and Darboux-Bäcklund transformations. The authors demonstrate the existence of purely fermionic nonlinear systems in \((2+1)\) dimensions.