TY - JOUR
T1 - The nonlinearized eigenvalue problem of the Toda hierarchy in the Lie–Poisson framework
AU - Du, Dianlou
AU - Cao, Cewen
AU - Wu, Yong Tang
N1 - Funding Information:
Project 19671074 was supported by National Natural Science Foundation of China. This work was partially supported by Hong Kong RGC/97-98/21. The first author also thanks the Natural Science Foundation of Henan for financial support.
Publisher copyright:
© 2000 Elsevier Science B.V. All rights reserved.
PY - 2000/10/1
Y1 - 2000/10/1
N2 - A 3 × 3 discrete eigenvalue problem associated with Toda hierarchy is presented. After the nonlinearization procedure, the 3 × 3 discrete eigenvalue problem is turned into an integrable Poisson map on the Poisson manifold R3N with a Lie-Poisson structure. As a reduction of the Lie-Poisson structure on the co-adjoint orbit, the standard symplectic structure on the symplectic manifold R2N is obtained. The Poisson map restricted on the leaves of the symplectic foliation is reduced to a usual symplectic map, which is exactly the nonlinearized 2 × 2 eigenvalue problem.
AB - A 3 × 3 discrete eigenvalue problem associated with Toda hierarchy is presented. After the nonlinearization procedure, the 3 × 3 discrete eigenvalue problem is turned into an integrable Poisson map on the Poisson manifold R3N with a Lie-Poisson structure. As a reduction of the Lie-Poisson structure on the co-adjoint orbit, the standard symplectic structure on the symplectic manifold R2N is obtained. The Poisson map restricted on the leaves of the symplectic foliation is reduced to a usual symplectic map, which is exactly the nonlinearized 2 × 2 eigenvalue problem.
UR - http://www.scopus.com/inward/record.url?scp=0034299785&partnerID=8YFLogxK
U2 - 10.1016/S0378-4371(00)00236-3
DO - 10.1016/S0378-4371(00)00236-3
M3 - Journal article
AN - SCOPUS:0034299785
SN - 0378-4371
VL - 285
SP - 332
EP - 350
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 3-4
ER -