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Inverse scattering transform for a supersymmetric Korteweg-de Vries equation

ABSTRACT
In this paper, the inverse scattering transform is extended to a super Korteweg-de Vries (KdV) equation with an arbitrary variable coefficient by using Kulish and Zeitlin’s approach. As a result, exact solutions of the super KdV equation are obtained. In the case of reflectionless potentials, the obtained exact solutions are reduced to soliton solutions. More importantly, based on the obtained results, an approach to extending the scattering transform is proposed for the supersymmetric KdV equation in the 1-dimensional Grassmann algebra. It is shown the approach can be applied to some other supersymmetric non-linear evolution equations in fluids.
KEYWORDS
PAPER SUBMITTED: 2018-05-12
PAPER REVISED: 2018-11-29
PAPER ACCEPTED: 2018-12-01
PUBLISHED ONLINE: 2019-03-31
DOI REFERENCE: https://doi.org/10.2298/TSCI180512081Z
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