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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/5258375 |
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| _version_ | 1832566889763569664 |
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| author | Mengshuang Tao Huanhe Dong |
| author_facet | Mengshuang Tao Huanhe Dong |
| author_sort | Mengshuang Tao |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-4895b2d451604e8982f708531423efb9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4895b2d451604e8982f708531423efb92025-02-03T01:02:46ZengWileyDiscrete 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 |
| spellingShingle | Mengshuang Tao Huanhe Dong Algebro-Geometric Solutions for a Discrete Integrable Equation Discrete Dynamics in Nature and Society |
| title | 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_short | Algebro-Geometric Solutions for a Discrete Integrable Equation |
| title_sort | algebro geometric solutions for a discrete integrable equation |
| url | http://dx.doi.org/10.1155/2017/5258375 |
| work_keys_str_mv | AT mengshuangtao algebrogeometricsolutionsforadiscreteintegrableequation AT huanhedong algebrogeometricsolutionsforadiscreteintegrableequation |