An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy

Yong-Tang Wu; Hongye Wang; Dianlou Du

doi:10.1088/0305-4470/35/17/311

An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy

Yong-Tang Wu, Hongye Wang, Dianlou Du^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

Abstract

A 3×3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2×2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.

Original language	English
Pages (from-to)	3971-3984
Number of pages	14
Journal	Journal of Physics A: Mathematical and General
Volume	35
Issue number	17
Early online date	19 Apr 2002
DOIs	https://doi.org/10.1088/0305-4470/35/17/311
Publication status	Published - 3 May 2002
Externally published	Yes

Scopus Subject Areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/35/17/311

Cite this

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abstract = "A 3×3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2×2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.",

author = "Yong-Tang Wu and Hongye Wang and Dianlou Du",

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N2 - A 3×3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2×2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.

AB - A 3×3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2×2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.

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An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy

Abstract

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