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

Abstract

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. PACS: 02.30.Ik, 02.30,Jr, 02.40.-k, 11.30.-j

arXiv comment7th International workshop "Group analysis of differential equations and integrable systems" (15-19 June 2014, Larnaca, Cyprus), 19 pages

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Cited by in corpus (1)

• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications