On the (Non)Removability of Spectral Parameters in Z2-Graded Zero-Curvature Representations and Its Applications

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 para...

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Bibliographic Details
Published inActa applicandae mathematicae Vol. 160; no. 1; pp. 129 - 167
Main Authors Kiselev, Arthemy V., Krutov, Andrey O.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 15.04.2019
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Probability Theory and Stochastic Processes
Supersymmetry
37K25
Frölicher–Nijenhuis bracket
Zero-curvature representation
Removability
Korteweg–de Vries equation
58J72
Spectral parameter
Gardner’s deformation
35Q53
58A50
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Summary: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.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-018-0198-6