The N=2 supersymmetric unconstrained matrix GNLS hierarchies

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

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    4 Citations (Scopus)
    35 Downloads (Pure)


    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
    Number of pages11
    Publication statusPublished - 2002

    Publication series

    PublisherDepartment of Applied Mathematics, University of Twente
    ISSN (Print)0169-2690


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


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