On the Lie-Poisson structure of the nonlinearized discrete eigenvalue problem

A 3 × 3 discrete eigenvalue problem and corresponding discrete soliton equations are proposed. Under a constraint between the potentials and eigenfunctions, the 3 × 3 discrete eigenvalue problem is nonlinearized into an integrable Poisson map with a Lie-Poisson structure. Further, a reduction of the Lie-Poisson structure on the co-adjoint orbit yields the standard symplectic structure. The Poisson map is reduced to the usual symplectic map when it is restricted on the leaves of the symplectic foliation.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Yongtang Wu, Dianlou Du; On the Lie–Poisson structure of the nonlinearized discrete eigenvalue problem. J. Math. Phys. 1 August 2000; 41 (8): 5832–5848. https://doi.org/10.1063/1.533440 and may be found at https://pubs.aip.org/aip/jmp/article/41/8/5832/814177/On-the-Lie-Poisson-structure-of-the-nonlinearized.