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On a Toda lattice hierarchy: Lax pair, integrable symplectic map and algebraic–geometric solution

Xiao Yang

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China

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and

Dianlou Du

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China

E-mail Address: ddl@zzu.edu.cn

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https://doi.org/10.1142/S021798491850344XCited by:0 (Source: Crossref)

Abstract

A Toda lattice hierarchy is studied by introducing a new spectral problem which is a discrete counterpart of the generalized Kaup–Newell spectral problem. Based on the Lenard recursion equation, Lax pair of the hierarchy is given. Further, the discrete spectral problem is nonlinearized into an integrable symplectic map. As a result, an algebraic–geometric solution in Riemann theta function of the hierarchy is obtained. Besides, two equations, the Volterra lattice and a (2+1)-dimensional Burgers equation with a discrete variable, yielded from the hierarchy are also solved.

Keywords:

PACS: 05.45.Yv, 02.30.Jr, 02.30.Ik, 04.20.Jb

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