Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice

We introduce two new discretizations of the Toda lattice related to the qd algorithm. They are demonstrated to belong to the same hierarchy as the continuous-time system, and to exemplify the general scheme for symplectic maps on Lie algebras with r-matrix Poisson brackets. The initial value problem...

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Bibliographic Details
Published in:Physics letters. A Vol. 206; no. 3; pp. 153 - 161
Main Author: Suris, Yuri B.
Format: Journal Article
Language:English
Published: Elsevier B.V 09.10.1995
ISSN:0375-9601, 1873-2429
Online Access:Get full text
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Summary:We introduce two new discretizations of the Toda lattice related to the qd algorithm. They are demonstrated to belong to the same hierarchy as the continuous-time system, and to exemplify the general scheme for symplectic maps on Lie algebras with r-matrix Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for both maps.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(95)00647-L