Geometric Bäcklund-Darboux transformations for the KP hierarchy

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

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    Abstract

    In this paper it is shown that, if you have two planes in the Sato Grassmannian that have an intersection of finite codimension, then the corresponding solutions of the KP hierarchy are linked by B\"acklund-Darboux (shortly BD-)transformations. The pseudodifferential operator that performs this transformation is shown to be built up in a geometric way from so-called elementary BD-transformations and is given here in a closed form. The corresponding action on the tau-function, associated to a plane in the Grassmannian, is also determined.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages33
    Publication statusPublished - 2000

    Publication series

    NameMemorandum Faculteit TW
    PublisherUniversity of Twente, Faculty of Applied Mathematics
    No.1556
    ISSN (Print)0169-2690

    Keywords

    • MSC-22E70
    • EWI-3376
    • MSC-81R10
    • METIS-141313
    • MSC-58G37
    • IR-65743
    • MSC-22E65
    • MSC-22E67
    • MSC-35Q58
    • MSC-35Q53

    Cite this

    Helminck, G. F., van de Leur, J. W., & van de Leur, J. W. (2000). Geometric Bäcklund-Darboux transformations for the KP hierarchy. (Memorandum Faculteit TW; No. 1556). Enschede: University of Twente, Department of Applied Mathematics.