Symmetries of supersymmetric CKP hierarchy and its reduction

Abstract

In this article, we construct supersymmetric C type Kadomtsev–Petviashvili (CKP) hierarchy and six-reduced supersymmetric CKP hierarchy and their additional symmetries. These additional flows of the supersymmetric CKP hierarchy constitute a C type SW1+∞ Lie algebra. Meanwhile, we find the six-reduced supersymmetric CKP hierarchy contains the super Sawada–Kotera equation as a primary equation. Lastly, we prove a fact that the additional C type SW1+∞ Lie algebraic structure is kept after doing the six-reduction from the supersymmetric CKP hierarchy.