Algebro-Geometric Solutions for a Discrete Integrable Equation

Algebro-Geometric Solutions for a Discrete Integrable Equation

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 wi...

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Main Authors: Mengshuang Tao, Huanhe Dong
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2017/5258375
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spelling doaj-4895b2d451604e8982f708531423efb92020-11-24T22:55:05ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/52583755258375Algebro-Geometric Solutions for a Discrete Integrable EquationMengshuang Tao0Huanhe Dong1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaWith 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.http://dx.doi.org/10.1155/2017/5258375
collection DOAJ
language English
format Article
sources DOAJ
author Mengshuang Tao
Huanhe Dong
spellingShingle Mengshuang Tao
Huanhe Dong
Algebro-Geometric Solutions for a Discrete Integrable Equation
Discrete Dynamics in Nature and Society
author_facet Mengshuang Tao
Huanhe Dong
author_sort Mengshuang Tao
title Algebro-Geometric Solutions for a Discrete Integrable Equation
title_short Algebro-Geometric Solutions for a Discrete Integrable Equation
title_full Algebro-Geometric Solutions for a Discrete Integrable Equation
title_fullStr Algebro-Geometric Solutions for a Discrete Integrable Equation
title_full_unstemmed Algebro-Geometric Solutions for a Discrete Integrable Equation
title_sort algebro-geometric solutions for a discrete integrable equation
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2017-01-01
description 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.
url http://dx.doi.org/10.1155/2017/5258375
work_keys_str_mv AT mengshuangtao algebrogeometricsolutionsforadiscreteintegrableequation
AT huanhedong algebrogeometricsolutionsforadiscreteintegrableequation
_version_ 1725657995775311872

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