A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies

G.F. Helminck

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    Abstract

    In this paper one considers the problem of finding solutions to a number of Toda-type hierarchies. All of them are associated with a commutative subalgebra of the $k \times k$-matrices. The first one is formulated in terms of upper triangular $\mathbb{Z} \times \mathbb{Z}$-matrices, the second one in terms of lower triangular ones and the third is a combination of the two foregoing types. It is shown that in an appropriate group setting solutions of the linearization of these Lax equations can be constructed by using the Birkhoff decomposition in the relevant group.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages16
    Publication statusPublished - 2004

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1745
    ISSN (Print)0169-2690

    Keywords

    • MSC-20G15
    • MSC-20G20
    • MSC-22E15
    • METIS-227111
    • EWI-3565
    • IR-65929
    • MSC-22E46

    Cite this

    Helminck, G. F. (2004). A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies. (Memorandum / Department of Applied Mathematics; No. 1745). Enschede: University of Twente, Department of Applied Mathematics.