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Abstract
In this paper, we construct a supersymmetric CKP(SCKP) hierarchy and its Darboux transformations. These Darboux transformations can generate new solutions from seed solutions by using supersymmetric functions. Further, we obtain the supersymmetric Sawada–Kotera equation from the reduction of supersymmetric CKP hierarchy. After that, using a new B type condition, we also construct a new supersymmetric BKP(SBKP) hierarchy which is different from the supersymmetric BKP hierarchy defined by Ramos and Stanciu. Meanwhile, the Darboux transformations of this new SBKP hierarchy are derived.
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