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

Y. Kodama; K. T-R McLaughlin

doi:10.1007/bf00400137

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

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.

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Y. Kodama, K. T-R McLaughlin. 1995-02-22. Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property. https://doi.org/10.1007/bf00400137

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