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

G.F. Helminck

    Research output: Book/ReportReportProfessional

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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.
    Helminck, G.F. / A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies. Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum / Department of Applied Mathematics; 1745).
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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.",
    keywords = "MSC-20G15, MSC-20G20, MSC-22E15, METIS-227111, EWI-3565, IR-65929, MSC-22E46",
    author = "G.F. Helminck",
    note = "Imported from MEMORANDA",
    year = "2004",
    language = "Undefined",
    series = "Memorandum / Department of Applied Mathematics",
    publisher = "University of Twente, Department of Applied Mathematics",
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    }

    Helminck, GF 2004, A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies. Memorandum / Department of Applied Mathematics, no. 1745, University of Twente, Department of Applied Mathematics, Enschede.

    A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies. / Helminck, G.F.

    Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum / Department of Applied Mathematics; No. 1745).

    Research output: Book/ReportReportProfessional

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    T1 - A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies

    AU - Helminck, G.F.

    N1 - Imported from MEMORANDA

    PY - 2004

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    N2 - 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.

    AB - 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.

    KW - MSC-20G15

    KW - MSC-20G20

    KW - MSC-22E15

    KW - METIS-227111

    KW - EWI-3565

    KW - IR-65929

    KW - MSC-22E46

    M3 - Report

    T3 - Memorandum / Department of Applied Mathematics

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

    PB - University of Twente, Department of Applied Mathematics

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    ER -

    Helminck GF. A factorization for $Z \times Z$-matrices yielding solutions of Toda-type hierarchies. Enschede: University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memorandum / Department of Applied Mathematics; 1745).