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Gardner's deformation of the Krasil'shchik-Kersten system
Arthemy V. Kiselev, Andrey O. Krutov
The classical problem of construction of Gardner's deformations for infinite-dimensional completely integrable systems of evolutionary partial differential equations (PDE) amounts…
Gardner's deformations as generators of new integrable systems
Arthemy V. Kiselev, Andrey O. Krutov
We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitio…
Gardner's deformations of the graded Korteweg-de Vries equations revisited
A. V. Kiselev, A. O. Krutov
We solve the Gardner deformation problem for the N=2 supersymmetric a=4 Korteweg-de Vries equation (P. Mathieu, 1988). We show that a known zero-curvature representation for this s…
Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
V. Hussin, A. V. Kiselev, A. O. Krutov +1
We prove that P.Mathieu's Open problem on constructing Gardner's deformation for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry invariant solutions, whe…