Gardner's deformation of the Krasil'shchik-Kersten system

The classical problem of construction of Gardner's deformations for infinite-dimensional completely integrable systems of evolutionary partial differential equations (PDE) amounts essentially to finding the recurrence relations between the integrals of motion. Using the correspondence between t...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 621; no. 1; pp. 12007 - 12025
Main Authors Kiselev, Arthemy V, Krutov, Andrey O
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 11.06.2015
Subjects
conservation laws
Deformation
Gardner's deformations
Integrable hierarchies
Krasil'shchik-Kersten system
Mathematical analysis
Partial differential equations
Physics
zero-curvature representations
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Summary:The classical problem of construction of Gardner's deformations for infinite-dimensional completely integrable systems of evolutionary partial differential equations (PDE) amounts essentially to finding the recurrence relations between the integrals of motion. Using the correspondence between the zero-curvature representations and Gardner deformations for PDE, we construct a Gardner's deformation for the Krasil'shchik-Kersten system. For this, we introduce the new nonlocal variables in such a way that the rules to differentiate them are consistent by virtue of the equations at hand and second, the full system of Krasil'shchik-Kersten's equations and the new rules contains the Korteweg-de Vries equation and classical Gardner's deformation for it.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/621/1/012007