Supersymmetric Integrable Systems:Backlund-Darboux Transformations And Discretizations

For the classical Boussinesq equation, a Backlund transformation consisting of four equations with an essential parameter is constructed; for the supersymmetric two-boson system, Backlund parameter is identified, the corresponding nonlinear su-perposition formula is constructed; for the supersymmetric KdV equation, a prop-er Darboux transformation is presented, integrable super differential-difference and difference-difference systems are constructed; for a generalized super KdV equation, three Backlund-Darboux transformations are worked out, three discrete systems to-gether with their Lax representations are provided, the reduction is considered for Kupershmidt’s super KdV equation, a nonlinear superposition formula is obtained for Levi’s Backlund transformation for the KdV equation; for the supersymmetric NLS equation, Darboux and Backlund transformations and integrable discretizations are presented, the integrable discretizations for supersymmetric MKdV equation are also obtained.