Bosonized Supersymmetric Sawada–Kotera Equations: Symmetries and Exact Solutions^*

The Bosonized Supersymmetric Sawada–Kotera (BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out.