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

Y. Kodama, K. T.R. McLaughlin

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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 language	English (US)
Pages (from-to)	37-47
Number of pages	11
Journal	Letters in Mathematical Physics
Volume	37
Issue number	1
DOIs	https://doi.org/10.1007/BF00400137
State	Published - 1996

Keywords

Initial-value problem
QR factorization
Toda hierarchy

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/BF00400137

Cite this

@article{db3f619320914817aa20a90a1f22009a,

title = "Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property",

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. 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 = "Initial-value problem, QR factorization, Toda hierarchy",

author = "Y. Kodama and McLaughlin, {K. T.R.}",

year = "1996",

doi = "10.1007/BF00400137",

language = "English (US)",

volume = "37",

pages = "37--47",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property

AU - Kodama, Y.

AU - McLaughlin, K. T.R.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - Initial-value problem

KW - QR factorization

KW - Toda hierarchy

UR - http://www.scopus.com/inward/record.url?scp=0039266788&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039266788&partnerID=8YFLogxK

U2 - 10.1007/BF00400137

DO - 10.1007/BF00400137

M3 - Article

AN - SCOPUS:0039266788

SN - 0377-9017

VL - 37

SP - 37

EP - 47

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this