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

作者:Wu YT; Wang HY; Du DL*
来源:Journal of Physics A: Mathematical and General , 2002, 35(17): 3971-3984.
DOI:10.1088/0305-4470/35/17/311

摘要

A 3 x 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 x 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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