THERMAL SCIENCE

International Scientific Journal

Sheng ZhangORCID

,

Caihong You

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 equation with an arbitrary variable coefficient by using Kulish and Zeitlin’s approach. As a result, exact solutions of the super Korteweg-de Vries 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 Korteweg-de Vries equation in the 1-D Grassmann algebra. It is shown the the approach can be applied to some other supersymmetric non-linear evolution equations in fluids.
KEYWORDS
Supersymmtric KdV equation, Grassmann algebra, inverse scattering transform method, scattering data, soliton solution
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
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [677 - 684]
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Inverse scattering transform for a supersymmetric Korteweg-de Vries equation

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