Gardner's deformations of the graded Korteweg-de Vries equations revisited

Abstract

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 superequation yields the system of new nonlocal variables such that their derivatives contain the Gardner deformation for the classical KdV equation.

References in corpus (2)

• Algebraic properties of Gardner's deformations for integrable systems
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation

Cited by in corpus (3)

• Gardner's deformation of the Krasil'shchik-Kersten system
• Gardner's deformations as generators of new integrable systems
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications