Crum Transformation and Wronskian Type Solutions for Supersymmetric KdV Equation
نویسنده
چکیده
Darboux transformation is reconsidered for the supersymmetric KdV system. By iterating the Darboux transformation, a supersymmetric extension of the Crum transformation is obtained for the Manin-Radul SKdV equation, in doing so one gets Wronskian superdeterminant representations for the solutions. Particular examples provide us explicit supersymmetric extensions, super solitons, of the standard soliton of the KdV equation. The KdV soliton appears as the body of the super soliton. On leave of absence from Beijing Graduate School, CUMT, Beijing 100083, China Supported by Beca para estancias temporales de doctores y tecnólogos extranjeros en España: SB95-A01722297 Partially supported by CICYT: proyecto PB92-019 1
منابع مشابه
Notes on solutions in Wronskian form to soliton equations: KdV-type
This paper can be an overview on solutions in Wronskian/Casoratian form to soliton equations with KdV-type bilinear forms. We first investigate properties of matrices commuting with a Jordan block, by which we derive explicit general solutions to equations satisfied by Wronskian/Casoratian entry vectors, which we call condition equations. These solutions are given according to the coefficient m...
متن کاملBinary Darboux-Bäcklund Transformations for Manin-Radul Super KdV Hierarchy
We construct the supersymmetric extensions of the Darboux-Bäcklund transformations (DBTs) for the Manin-Radul super KdV hierarchy using the super-pseudo-differential operators. The elementary DBTs are triggered by the gauge operators constructed from the wavefunctions and adjoint wavefunctions of the hierarchy. Iterating these elementary DBTs, we obtain not only Wronskian type but also binary t...
متن کاملBinary Darboux-Bäcklund Transformations for the Manin-Radul Super KdV Hierarchy
We construct the supersymmetric extensions of the Darboux-Bäcklund transformations (DBTs) for the Manin-Radul super KdV hierarchy using the super-pseudo-differential operators. The elementary DBTs are triggered by the gauge operators constructed from the wave functions and adjoint wave functions of the hierarchy. Iterating these elementary DBTs, we obtain not only Wronskian type but also binary...
متن کاملA Note on the Third Family of N = 2 Supersymmetric KdV
We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular , the third family of N = 2 KdV hierarchies is recovered. We also give an easy construction of Wronskian solutions of the KP and KdV type equations.
متن کاملNonlinear superposition Formulae for supersymmetric KdV Equation
In this paper, we derive a Bäcklund transformation for the supersymmetric Kortwegde Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Kortweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 1984....
متن کامل