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.
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.",
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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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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.

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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

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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).