Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property

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Abstract

We give an explicit formula for the solution to the initial-value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szegö, and is also interpreted as a consequence of the QR factorization method of Symes. The sorting property of the dynamics is also proved for the case of a generic symmetric matrix in the sense described in the text, and generalizations of tridiagonal formulae are given for the case of matrices with 2M + 1 nonzero diagonals.

Original languageEnglish (US)
Pages (from-to)37-47
Number of pages11
JournalLetters in Mathematical Physics
Volume37
Issue number1
DOIs
StatePublished - Jan 1 1996

Keywords

  • Initial-value problem
  • QR factorization
  • Toda hierarchy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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