The nonlinearized eigenvalue problem of the Toda hierarchy in the Lie–Poisson framework

Dianlou Du, Cewen Cao and Yong-Tang Wu

Physica A: Statistical Mechanics and its Applications, 2000, vol. 285, issue 3, 332-350

Abstract: 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.

Keywords: Poisson map; Lie–Poisson structure; Symplectic foliation; Symplectic map (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:285:y:2000:i:3:p:332-350

DOI: 10.1016/S0378-4371(00)00236-3

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