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.
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Research Article| October 03 2012
Gardner's deformations of the graded Korteweg–de Vries equations revisited
A. V. Kiselev;
A. V. Kiselev, A. O. Krutov; Gardner's deformations of the graded Korteweg–de Vries equations revisited. J. Math. Phys. 1 October 2012; 53 (10): 103511. https://doi.org/10.1063/1.4754288
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