Supersymmetric KdV equation: Darboux transformation and discrete systems. (English) Zbl 1286.35224
A proper Darboux transformation is presented for the supersymmetric KdV equation. This Darboux transformation leads to the Bäcklund transformation found earlier by Q. P. Liu and Y. F. Xie [Phys. Lett., A 325, No. 2, 139–143 (2004; Zbl 1161.37344)]. The Darboux transformation and the related Bäcklund transformation are used to construct integrable super differential-difference and difference-difference systems. The continuum limits of these discrete systems and of their Lax pairs are also considered.
Reviewer: Masataka Kanki (Tokyo)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 81Q60 | Supersymmetry and quantum mechanics |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
