### 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 |

State | Published - 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Initial-value problem
- QR factorization
- Toda hierarchy

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Letters in Mathematical Physics*,

*37*(1), 37-47.

**Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property.** / Kodama, Y.; Mclaughlin, Kenneth D T.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 37, no. 1, pp. 37-47.

}

TY - JOUR

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

AU - Kodama, Y.

AU - Mclaughlin, Kenneth D T

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

M3 - Article

AN - SCOPUS:0039266788

VL - 37

SP - 37

EP - 47

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -