Elementary Darboux transformations for the $n$-component $KP$-hierarchy

G.F. Helminck, J.W. van de Leur, J.W. van de Leur

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    Abstract

    In this paper a purely algebraic setting is described in which a characterization of the dual wavefunctions of the multicomponent $KP$-hierarchy and an interpretation of the bilinear form of this system of nonlinear equations can be given. The framework enables the construction of solutions starting from a matrix version of the Sato Grassmannian and the expression in formal power series determinants, the so-called $\tau$-functions. This leads to a geometric description of the elementary Darboux transformations for the $n$-component $KP$-hierarchy and one concludes with showing how to construct them, both at the differential operator level as at the $\tau$-function level.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages22
    Publication statusPublished - 2002

    Publication series

    NameMemorandum Faculty Mathematical Sciences
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1645
    ISSN (Print)0169-2690

    Keywords

    • METIS-208643
    • MSC-22E65
    • MSC-35Q58
    • EWI-3465
    • MSC-58B25
    • IR-65831
    • MSC-22E70

    Cite this

    Helminck, G. F., van de Leur, J. W., & van de Leur, J. W. (2002). Elementary Darboux transformations for the $n$-component $KP$-hierarchy. (Memorandum Faculty Mathematical Sciences; No. 1645). Enschede: University of Twente, Department of Applied Mathematics.