dorsal/arxiv
View SchemaExplicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property
| Authors | Y. Kodama, K. T-R McLaughlin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9502006 |
| URL | https://arxiv.org/abs/solv-int/9502006 |
| DOI | 10.1007/BF00400137 |
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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"abstract": "We give an explicit formula for the solution to the initial value problem of\nthe full symmetric Toda hierarchy. The formula is obtained by the\northogonalization procedure of Szeg\\\"{o}, and is also interpreted as a\nconsequence of the QR factorization method of Symes \\cite{symes}. The sorting\nproperty of the dynamics is also proved for the case of a generic symmetric\nmatrix in the sense described in the text, and generalizations of tridiagonal\nformulae are given for the case of matrices with $2M+1$ nonzero diagonals.",
"arxiv_id": "solv-int/9502006",
"authors": [
"Y. Kodama",
"K. T-R McLaughlin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1007/BF00400137",
"title": "Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property",
"url": "https://arxiv.org/abs/solv-int/9502006"
},
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