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

Abstract

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 Frölicher--Nijenhuis bracket.

38 pages, accepted to Acta Appl. Math

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