TY - JOUR

T1 - Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice

AU - Suris, Yuri B.

N1 - Funding Information:
I thank the authors of Ref. \[1 4\] for sending me their paper prior to publication; it influenced considerably the final version of the present Letter. I am grateful also to Frank Nijhoff for useful remarks. The research of the author is financially supported by the Deutsche Forschungsgemeinschaft.

PY - 1995/10/9

Y1 - 1995/10/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000404004&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(95)00647-L

DO - 10.1016/0375-9601(95)00647-L

M3 - Article

AN - SCOPUS:0000404004

SN - 0375-9601

VL - 206

SP - 153

EP - 161

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3-4

ER -