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

Y. Kodama; K. T-R McLaughlin

doi:10.1007/BF00400137

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

solv-int 2016-09-08 v1 Exactly Solvable and Integrable Systems

Authors: Y. Kodama , K. T-R McLaughlin

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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 Szeg\"{o}, and is also interpreted as a consequence of the QR factorization method of Symes \cite{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.

Keywords

symmetric toda hierarchy explicit integration initial value problem orthogonalization qr factorization sorting property

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@article{arxiv.solv-int/9502006,
  title  = {Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property},
  author = {Y. Kodama and K. T-R McLaughlin},
  journal= {arXiv preprint arXiv:solv-int/9502006},
  year   = {2016}
}

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13 pages, Latex.

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

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