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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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