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

We solve the Gardner deformation problem for the N = 2 supersymmetric a = 4 Korteweg–de Vries equation [P. Mathieu, “Supersymmetric extension of the Korteweg–de Vries equation,” J. Math. Phys. 29(11), 2499–2506 (1988)]. We show that a known zero-curvature representation for this super-equation yields the system of new nonlocal variables such that their derivatives contain the Gardner deformation for the classical KdV equation.