A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation
An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established. Liouville integrability for the obtained family of discrete Hamiltonian sys...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/4152917 |
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| author | Xi-Xiang Xu Meng Xu |
| author_facet | Xi-Xiang Xu Meng Xu |
| author_sort | Xi-Xiang Xu |
| collection | DOAJ |
| description | An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established. Liouville integrability for the obtained family of discrete Hamiltonian systems is proved. Based on the gauge transformation between the Lax pair, a Darboux-Bäcklund transformation of the first nonlinear different-difference equation in obtained family is deduced. Using this Darboux-Bäcklund transformation, an exact solution is presented. |
| format | Article |
| id | doaj-art-d90cbad8cca54a7cab8e9ec693738046 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d90cbad8cca54a7cab8e9ec6937380462025-02-03T07:25:38ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/41529174152917A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund TransformationXi-Xiang Xu0Meng Xu1College 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, ChinaAn integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established. Liouville integrability for the obtained family of discrete Hamiltonian systems is proved. Based on the gauge transformation between the Lax pair, a Darboux-Bäcklund transformation of the first nonlinear different-difference equation in obtained family is deduced. Using this Darboux-Bäcklund transformation, an exact solution is presented.http://dx.doi.org/10.1155/2018/4152917 |
| spellingShingle | Xi-Xiang Xu Meng Xu A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation Discrete Dynamics in Nature and Society |
| title | A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation |
| title_full | A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation |
| title_fullStr | A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation |
| title_full_unstemmed | A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation |
| title_short | A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation |
| title_sort | family of integrable different difference equations its hamiltonian structure and darboux backlund transformation |
| url | http://dx.doi.org/10.1155/2018/4152917 |
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