Abstract
We develop a pseudo-differential approach to the N = 2 supersymmetric unconstrained matrix (k|n, m)-generalized nonlinear Schrödinger hierarchies and prove consistency of the corresponding Lax-pair representation (nlin.SI/0201026). Furthermore, we establish their equivalence to the integrable hierarchies derived in the super-algebraic approach of the homogeneously-graded loop superalgebra \({sl(2k{+}n\vert 2k{+}m)\otimes C[{\lambda},{\lambda}^{-1}]}\) (nlin.SI/0206037). We introduce an unconventional definition of N = 2 supersymmetric strictly pseudo-differential operators so as to close their algebra among themselves.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Sorin, A.S., Kersten, P.H.M.: The N =2 supersymmetric unconstrained matrix GNLS hierarchies. Lett. Math. Phys. 60, 135–146 (2002). nlin.SI/0201026
Delduc, F., Sorin, A.S.: Recursion operators of the N = 2 supersymmetric unconstrained matrix GNLS hierarchies. In: JHEP Proceedings, PrHEP unesp2002, Workshop on Integrable Theories, Solitons and Duality, Sao Paulo 1–6 July 2002, 10p. nlin.SI/0206037
Bonora, L., Krivonos, S., Sorin, A.: The N =2 supersymmetric matrix GNLS hierarchies. Lett. Math. Phys. 45, 63–79 (1998). solv-int/9711009
Bonora, L., Krivonos, S., Sorin, A.: Coset approach to the N = 2 supersymmetric matrix GNLS hierarchies. Phys. Lett. A240, 201–212 (1998). solv-int/9711012
Bonora, L., Krivonos, S., Sorin, A.: Towards the construction of N =2 supersymmetric integrable hierarchies. Nucl. Phys. B477, 835–854 (1996). hep-th/9604165
Bonora, L., Sorin, A.: The Hamiltonian structure of the N =2 supersymmetric GNLS hierarchy. Phys. Lett. B407, 131–142 (1997). hep-th/9704130
Popowicz, Z.: The extended supersymmetrization of the multicomponent Kadomtsev Petviashvili hierarchy. J. Phys. A29, 1281–1292 (1996). hep-th/9510185
Fordy, A.P., Kulish, P.P.: Nonlinear Schrödinger equations and simple Lie algebras. Commun. Math. Phys. 89, 427–443 (1983)
Kersten, P.H.M., Sorin, A.S.: Bi-Hamiltonian structure of the N =2 supersymmetric N = 2 supersymmetric α=1 KdV hierarchy. Phys. Lett. A300, 397–406 (2002). nlin.SI/0201061
Aratyn, H., Gomes, J.F., Nissimov, E., Pacheva, S., Zimerman, A.H.: Symmetry flows, conservation laws and dressing approach to the integrable models. In: Aratyn, H., Sorin, A.S. (eds.) Integrable Hierarchies and Modern Physical Theories, pp. 243–275, Kluwer Academic Publication, Dordrecht/ (2001). nlin.SI/0012042
Aratyn, H., Gomes, J.F., de Castro, G.M., Silka, M.B., Zimerman, A.H.: Supersymmetry for integrable hierarchies on loop superalgebras. J. Phys. A38, 9341–9358 (2005). hep-th/0508008
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Delduc, F., Lechtenfeld, O. & Sorin, A.S. N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies are Consistent. Lett Math Phys 84, 109–122 (2008). https://doi.org/10.1007/s11005-008-0237-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11005-008-0237-8