The N=2 supersymmetric unconstrained matrix GNLS hierarchies

A.S. Sorin, P.H.M. Kersten

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    4 Citations (Scopus)
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    Abstract

    The generalization of the $N=2$ supersymmetric chiral matrix $(k|n,m)$--GNLS hierarchy to the case when matrix entries are bosonic and fermionic unconstrained $N=2$ superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of $N=2$ unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral $N=2$ superfields, it reproduces the $N=2$ chiral matrix $(k|n,m)$-GNLS hierarchy, while in the scalar case, $k=1$, it is equivalent to the $N=2$ supersymmetric multicomponent hierarchy. The simplest example --- the $N=2$ unconstrained $(1|1,0)$--GNLS hierarchy --- and its reduction to the $N=2$ supersymmetric ${\alpha}=1$ KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages11
    Publication statusPublished - 2002

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1613
    ISSN (Print)0169-2690

    Keywords

    • MSC-35Q51
    • MSC-35Q53
    • IR-65800
    • EWI-3433
    • MSC-35Q58
    • Completely integrable systems
    • Discrete symmetries
    • Supersymmetry

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  • Cite this

    Sorin, A. S., & Kersten, P. H. M. (2002). The N=2 supersymmetric unconstrained matrix GNLS hierarchies. (Memorandum; No. 1613). Enschede: University of Twente, Department of Applied Mathematics.