Spaces of boundary values related to a multipoint version of the KP-hierarchy

G.F. Helminck

    Research output: Book/ReportReportProfessional

    39 Downloads (Pure)

    Abstract

    In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of the $KP$-hierarchy. These Grassmann manifolds are built in such a way that the determinant line bundle and its dual over them still make sense. The same holds for the so-called $\tau$-functions, determinants of certain Fredholm operators that measure the failure of equivariance at lifting the commuting flows of ths hierarchy to these bundles. Solutions of the linearization are described by wave functions of a certain type. They are perturbations of the trivial solution with the leading term of the perturbation determining the type. One concludes with showing that, if a plane in the Grassmann manifold yields wave functions of different types, they are connected by a differential operator in the coordinates of the flows.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages16
    Publication statusPublished - 2004

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1744
    ISSN (Print)0169-2690

    Keywords

    • MSC-22E70
    • MSC-58B25
    • IR-65928
    • MSC-35Q58
    • MSC-22E65
    • METIS-227110
    • EWI-3564

    Cite this

    Helminck, G. F. (2004). Spaces of boundary values related to a multipoint version of the KP-hierarchy. (Memorandum; No. 1744). Enschede: University of Twente, Department of Applied Mathematics.
    Helminck, G.F. / Spaces of boundary values related to a multipoint version of the KP-hierarchy. Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum; 1744).
    @book{c3029e1cc64344c58901fb44300a952c,
    title = "Spaces of boundary values related to a multipoint version of the KP-hierarchy",
    abstract = "In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of the $KP$-hierarchy. These Grassmann manifolds are built in such a way that the determinant line bundle and its dual over them still make sense. The same holds for the so-called $\tau$-functions, determinants of certain Fredholm operators that measure the failure of equivariance at lifting the commuting flows of ths hierarchy to these bundles. Solutions of the linearization are described by wave functions of a certain type. They are perturbations of the trivial solution with the leading term of the perturbation determining the type. One concludes with showing that, if a plane in the Grassmann manifold yields wave functions of different types, they are connected by a differential operator in the coordinates of the flows.",
    keywords = "MSC-22E70, MSC-58B25, IR-65928, MSC-35Q58, MSC-22E65, METIS-227110, EWI-3564",
    author = "G.F. Helminck",
    note = "Imported from MEMORANDA",
    year = "2004",
    language = "Undefined",
    series = "Memorandum",
    publisher = "University of Twente, Department of Applied Mathematics",
    number = "1744",

    }

    Helminck, GF 2004, Spaces of boundary values related to a multipoint version of the KP-hierarchy. Memorandum, no. 1744, University of Twente, Department of Applied Mathematics, Enschede.

    Spaces of boundary values related to a multipoint version of the KP-hierarchy. / Helminck, G.F.

    Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum; No. 1744).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Spaces of boundary values related to a multipoint version of the KP-hierarchy

    AU - Helminck, G.F.

    N1 - Imported from MEMORANDA

    PY - 2004

    Y1 - 2004

    N2 - In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of the $KP$-hierarchy. These Grassmann manifolds are built in such a way that the determinant line bundle and its dual over them still make sense. The same holds for the so-called $\tau$-functions, determinants of certain Fredholm operators that measure the failure of equivariance at lifting the commuting flows of ths hierarchy to these bundles. Solutions of the linearization are described by wave functions of a certain type. They are perturbations of the trivial solution with the leading term of the perturbation determining the type. One concludes with showing that, if a plane in the Grassmann manifold yields wave functions of different types, they are connected by a differential operator in the coordinates of the flows.

    AB - In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of the $KP$-hierarchy. These Grassmann manifolds are built in such a way that the determinant line bundle and its dual over them still make sense. The same holds for the so-called $\tau$-functions, determinants of certain Fredholm operators that measure the failure of equivariance at lifting the commuting flows of ths hierarchy to these bundles. Solutions of the linearization are described by wave functions of a certain type. They are perturbations of the trivial solution with the leading term of the perturbation determining the type. One concludes with showing that, if a plane in the Grassmann manifold yields wave functions of different types, they are connected by a differential operator in the coordinates of the flows.

    KW - MSC-22E70

    KW - MSC-58B25

    KW - IR-65928

    KW - MSC-35Q58

    KW - MSC-22E65

    KW - METIS-227110

    KW - EWI-3564

    M3 - Report

    T3 - Memorandum

    BT - Spaces of boundary values related to a multipoint version of the KP-hierarchy

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Helminck GF. Spaces of boundary values related to a multipoint version of the KP-hierarchy. Enschede: University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum; 1744).