N = 2 Supersymmetric unconstrained matrix GNLS hierarchies are consistent

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  • École normale supérieure de Lyon (ENS de Lyon)
  • Joint Institute for Nuclear Research (JINR)
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OriginalspracheEnglisch
Seiten (von - bis)109-122
Seitenumfang14
FachzeitschriftLetters in mathematical physics
Jahrgang84
Ausgabenummer2-3
PublikationsstatusVeröffentlicht - Juni 2008

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|2k+m) ⊗ C[λ,λ-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.

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N = 2 Supersymmetric unconstrained matrix GNLS hierarchies are consistent. / Delduc, Francois; Lechtenfeld, Olaf; Sorin, Alexander S.
in: Letters in mathematical physics, Jahrgang 84, Nr. 2-3, 06.2008, S. 109-122.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Delduc F, Lechtenfeld O, Sorin AS. N = 2 Supersymmetric unconstrained matrix GNLS hierarchies are consistent. Letters in mathematical physics. 2008 Jun;84(2-3):109-122. doi: 10.1007/s11005-008-0237-8
Delduc, Francois ; Lechtenfeld, Olaf ; Sorin, Alexander S. / N = 2 Supersymmetric unconstrained matrix GNLS hierarchies are consistent. in: Letters in mathematical physics. 2008 ; Jahrgang 84, Nr. 2-3. S. 109-122.
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abstract = "We develop a pseudo-differential approach to the N = 2 supersymmetric unconstrained matrix (k|n, m)-generalized nonlinear Schr{\"o}dinger 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|2k+m) ⊗ C[λ,λ-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.",
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AU - Delduc, Francois

AU - Lechtenfeld, Olaf

AU - Sorin, Alexander S.

N1 - Funding Information: A.S. would like to thank the Laboratoire de Physique de l’ENS Lyon and Insti-tut für Theoretische Physik, Universität Hannover, for the hospitality during the course of this work. This work was partially supported by the RFBR Grant No. 06-01-00627-a, RFBR-DFG Grant No. 06-02-04012-a, DFG Grant 436 RUS 113/669-3, the Program for Supporting Leading Scientific Schools (Grant No. NSh-5332.2006.2), and by the Heisenberg-Landau Program. Finally, we are grateful to the anonymous referee for his critical questions and a very careful reading of the manuscript. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

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N2 - 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|2k+m) ⊗ C[λ,λ-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.

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KW - Completely integrable systems

KW - Discrete symmetries

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