Abstract
The N = 2 supersymmetric extension of KdV-equation is discussed. For the most intriguing case N = 2, a = 1, hierarchies of conservation laws, even and odd symmetries are constructed.Moreover the recursion on the odd hierarchies is given.
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References
P. Labelle and P. Mathieu, A new N = 2 supersymmetric Korteweg-de Vries equation, J.Math.Phys., 32(4):923–927, 1991.
G.H.M. Roelofs, prolongation structures of Supersymmetric Systems, Ph.D. Thesis, Department of Applied Mathematics, University of Twente, Enschede, the Netherlands, 1993.
Z. Popowicz, The Lax formulaton of the “new “ N = 2 SUSY KdV equation, Phys.Lett. A, 174(5-6):411–415, 1993.
P.H.M. Kersten, Higher order supersymmetries and fermionic conservation laws of the supersymmetric extension of the KdV equation, Phys.Lett. A, 134(1):25–30, 1988.
I.S. Krasil’shchik, Complete Integrability of nonlinear PDE and Supersymmetry, Proceedings: Lie Groups, Geometric Structures and Differential Equations-One Hundred Years after Sophus Lie-RIMS Kokyuroku 1150, Kyoto University, Kyoto, Japan, 2000 (pp.147–152)
Kersten, Paul.H.M.; Supersymmetries and Recursion Operators for N=2 supersymmetric KdV-equation Proceedings: Lie Groups, Geometric Structures and Differential Equations-One Hundred Years after Sophus Lie-RIMS Kokyuroku 1150, Kyoto University, Kyoto, Japan, 2000 (pp.153–161)
I.S. Krasil’shchik and P.H.M. Kersten, Symmetries and Recursion Operators for Classical and Supersymmetric differential Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
P.H.M. Kersten and I.S. Krasil’shchik, Complete Integrability of a coupled KdV-MKdV Sytem, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, to appear, 2001
S. Krivonos, A. Sorin. Extended N = 2 supersymmetric matrix (1, s)-KdV hierarchies. Phys. Lett. A251 (1999) 109.
P. Mathieu. Open problems for the super KdV equation. AARMS-CRM Workshop on Baecklund and Darboux transformations. The Geometry of Soliton Theory. June 4-9, 1999. Halifax, Nova Scotia.
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Kersten, P.H.M. (2001). Symmetries and Recursions For N = 2 Supersymmetric KDV-Equation. In: Aratyn, H., Sorin, A.S. (eds) Integrable Hierarchies and Modern Physical Theories. NATO Science Series, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0720-7_11
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DOI: https://doi.org/10.1007/978-94-010-0720-7_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6963-9
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