Algebro-Geometric Solutions for a Discrete Integrable Equation

Mengshuang Tao and Huanhe Dong

Discrete Dynamics in Nature and Society, 2017, vol. 2017, 1-9

Abstract:

With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. By means of discrete zero curvature equation, we obtain a discrete integrable hierarchy. According to decomposition of the discrete systems, the new differential-difference integrable systems with two-potential functions are derived. By constructing the Abel-Jacobi coordinates to straighten the continuous and discrete flows, the Riemann theta functions are proposed. Based on the Riemann theta functions, the algebro-geometric solutions for the discrete integrable systems are obtained.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:5258375

DOI: 10.1155/2017/5258375

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