Geodesic
Group-theoretical structure and inverse scattering method for super-KdV equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 17, Tome 291 (2002), pp. 185-205

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Using group-theoretical approach to the inverse scattering method the super-Korteveg-de Vries equation is obtained by application of the Drinfeld–Sokolov reduction to $osp(1|2)$ loop super-algebra. The direct and inverse scattering problems are discussed for the corresponding Lax pair. 
@article{ZNSL_2002_291_a10,
     author = {P. P. Kulish and A. M. Zeitlin},
     title = {Group-theoretical structure and inverse scattering method for {super-KdV} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {185--205},
     publisher = {mathdoc},
     volume = {291},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a10/}
}
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P. P. Kulish; A. M. Zeitlin. Group-theoretical structure and inverse scattering method for super-KdV equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 17, Tome 291 (2002), pp. 185-205. http://geodesic.mathdoc.fr/item/ZNSL_2002_291_a10/