$\tau$-Functions for a two-point version of the $KP$-hierarchy

G.F. Helminck

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    Abstract

    In this paper a multipoint version of the linearization of the $KP$-hierarchy is described. Solutions of this system in the form of wave functions are constructed starting from a suitable Grassmann manifold and a group of commuting flows corresponding to the configuration of $n$ points in $\mathbb{C}$. The failure of equivariance at lifting these flows to the determinant bundle over this Grassmann manifold is measured by the determinants of certain Fredholm operators, the so-called $\tau$-functions. In the case of two points an explicit relation between these $\tau$-functions and the wave functions is derived.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages15
    Publication statusPublished - 2003

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1671
    ISSN (Print)0169-2690

    Keywords

    • MSC-35Q53
    • MSC-35Q58
    • MSC-22E65
    • METIS-211955
    • MSC-58B25
    • IR-65856
    • EWI-3491
    • MSC-22E70

    Cite this

    Helminck, G. F. (2003). $\tau$-Functions for a two-point version of the $KP$-hierarchy. (Memorandum; No. 1671). Enschede: University of Twente, Department of Applied Mathematics.