On integrability aspects of the supersymmetric sine-Gordon equation
arXiv:1703.07925 · doi:10.1088/1751-8121/aa6324
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-Bäcklund 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.
References in corpus (7)
- A supersymmetric Sawada-Kotera equation
- On Darboux transformation of the supersymmetric sine-Gordon equation
- On linearization of super sine-Gordon equation
- Permutability of Backlund Transformation for N=1 Supersymmetric Sinh-Gordon
- On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
- Supersymmetric versions of the equations of conformally parametrized surfaces
- Supersymmetric versions of the Fokas-Gel'fand formula for immersion