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

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Abstract

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.

Original languageEnglish
Pages (from-to)153-161
Number of pages9
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume206
Issue number3-4
DOIs
StatePublished - 9 Oct 1995
Externally publishedYes

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