Gardner's deformation of the Krasil'shchik-Kersten system
arXiv:1409.6688 · doi:10.1088/1742-6596/621/1/012007
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
7th International workshop "Group analysis of differential equations and integrable systems" (15-19 June 2014, Larnaca, Cyprus), 19 pages