On the (Non)Removability of Spectral Parameters in Z 2 -Graded Zero-Curvature Representations and Its Applications

Arthemy V. Kiselev, Andrey O. Krutov*

*Corresponding author for this work

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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 languageEnglish
Pages (from-to)129-167
Number of pages39
JournalActa applicandae mathematicae
Issue number1
Publication statusPublished - 15-Apr-2019


  • Frölicher–Nijenhuis bracket
  • Gardner’s deformation
  • Korteweg–de Vries equation
  • Removability
  • Spectral parameter
  • Supersymmetry
  • Zero-curvature representation

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