On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications

• Main Authors: Kiselev, Arthemy V, Krutov, Andrey O
• Format: Journal Article
• Language: English
• Published: 30.01.2013
• Subjects: Mathematics - Differential Geometry; Physics - Exactly Solvable and Integrable Systems
• DOI: 10.48550/arxiv.1301.7143

Acta Appl. Math. (2019) Vol.160, n.1, 129--167 We generalise to the $\mathbb{Z}_2$-graded set-up a practical method for inspecting the (non)removability of parameters in zero-curvature representations for partial differential equations (PDEs) under the action of smooth families of gauge transformations. We illustrate the generation and elimination of parameters in the flat structures over $\mathbb{Z}_2$-graded PDEs by analysing the link between deformation of zero-curvature representations via infinitesimal gauge transformations and, on the other hand, propagation of linear coverings over PDEs using the Fr\"olicher--Nijenhuis bracket.