N=2 and N=4 Supersymmetric mKdV and sinh-Gordon Hierarchies
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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.
25 pages
25 pages