Geodesic
Bäcklund–Darboux Transformations and Discretizations of Super KdV Equation
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: super integrable systems; KdV; Bäcklund–Darboux transformations; discrete integrable systems. 
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     author = {Ling-Ling Xue and Qing Ping Liu},
     title = {B\"acklund{\textendash}Darboux {Transformations} and {Discretizations} of {Super} {KdV} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a44/}
}
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Ling-Ling Xue; Qing Ping Liu. Bäcklund–Darboux Transformations and Discretizations of Super KdV Equation. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a44/

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