Bäcklund–Darboux Transformations and Discretizations of Super KdV Equation
نویسندگان
چکیده
For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund–Darboux transformations and the corresponding discrete system are considered for Kupershmidt’s super KdV equation. When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi’s Bäcklund transformation for the KdV equation.
منابع مشابه
Binary 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 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 کاملDarboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.
متن کاملExplicit multiple singular periodic solutions and singular soliton solutions to KdV equation
Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...
متن کاملCrum Transformation and Wronskian Type Solutions for Supersymmetric KdV Equation
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...
متن کامل