Abstract
We generalise to the 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 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.
Original language | English |
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Pages (from-to) | 129-167 |
Number of pages | 39 |
Journal | Acta applicandae mathematicae |
Volume | 160 |
Issue number | 1 |
DOIs | |
Publication status | Published - 15-Apr-2019 |
Keywords
- Frölicher–Nijenhuis bracket
- Gardner’s deformation
- Korteweg–de Vries equation
- Removability
- Spectral parameter
- Supersymmetry
- Zero-curvature representation