N=2 and N=4 Supersymmetric mKdV and sinh-Gordon Hierarchies
  Integrable models with higher N=2 and N=4 supersymmetries are formulated on reductions of twisted loop superalgebras $\hat{sl}(2|2)$ and $\hat{sl}(4|4) $ endowed with principal gradation. In case of the $\hat{sl}(4|4)$ loop algebra a sequence of progressing reductions leads both to the N=4 and N=2 supersymmetric mKdV and sinh-Gordon equations.   The reduction scheme is induced by twisted automorphism and allows via dressing approach to associate to each symmetry flow of half-integer degree a supersymmetry transformation involving only local expressions in terms of the underlying fields. 
H. Aratyn, J.F. Gomes, L.H. Ymai and A.H. Zimerman