Large-Data Solutions in a Three-Dimensional Chemotaxis-Haptotaxis System with Remodeling of Non-diffusible Attractant: The Role of Sub-linear Production of Diffusible Signal

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.