Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 045, 10 pages      arXiv:1312.6976      https://doi.org/10.3842/SIGMA.2014.045

Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation

Ling-Ling Xue and Qing Ping Liu
Department of Mathematics, China University of Mining and Technology, Beijing 100083, P. R. China

Received January 02, 2014, in final form April 10, 2014; Published online April 17, 2014

Abstract
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.

Key words: super integrable systems; KdV; Bäcklund-Darboux transformations; discrete integrable systems.

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