On integrability aspects of the supersymmetric sine-Gordon equation
Abstract
In this paper we study certain integrability properties of the supersymmetric sine-Gordon equation. We construct Lax pairs with their zero-curvature representations which are equivalent to the supersymmetric sine-Gordon equation. From the fermionic linear spectral problem, we derive coupled sets of super Riccati equations and the auto-B\"acklund transformation of the supersymmetric sine-Gordon equation. In addition, a detailed description of the associated Darboux transformation is presented and non-trivial super multisoliton solutions are constructed. These integrability properties allow us to provide new explicit geometric characterizations of the bosonic supersymmetric version of the Sym--Tafel formula for the immersion of surfaces in a Lie superalgebra. These characterizations are expressed only in terms of the independent bosonic and fermionic variables.
Keywords
Cite
@article{arxiv.1703.07925,
title = {On integrability aspects of the supersymmetric sine-Gordon equation},
author = {Sébastien Bertrand},
journal= {arXiv preprint arXiv:1703.07925},
year = {2017}
}