On Darboux transformation of the supersymmetric sine-Gordon equation
M. Siddiq, M. Hassan, U. Saleem
TL;DR
This paper develops a Darboux transformation for the super sine-Gordon equation, linking it to super Bäcklund transformations and generating multi-soliton solutions in the supersymmetric context.
Contribution
It introduces a Darboux transformation for superfields of the super sine-Gordon equation, enabling the construction of super soliton solutions and establishing a connection with super Bäcklund transformations.
Findings
Darboux transformation for super sine-Gordon equation constructed
Relation established between Darboux and super Bäcklund transformations
Explicit N super soliton solutions obtained
Abstract
Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super B\"{a}cklund transformation and is further used to obtain super soliton solutions.
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