Abstract

We consider the problem of constructing Gardner’s deformations for the N = 2 supersymmetric a = 4-Korteweg–de Vries (SKdV) equation; such deformations yield recurrence relations between the super-Hamiltonians of the hierarchy. We prove the nonexistence of supersymmetry-invariant deformations that retract to Gardner’s formulas for the Korteweg-de Vries (KdV) with equation
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