Generalized Matrix Exponential Solutions to the AKNS Hierarchy
Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solu...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/1375653 |
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| _version_ | 1850110405606637568 |
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| author | Jian-bing Zhang Canyuan Gu Wen-Xiu Ma |
| author_facet | Jian-bing Zhang Canyuan Gu Wen-Xiu Ma |
| author_sort | Jian-bing Zhang |
| collection | DOAJ |
| description | Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different kinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy are also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure. |
| format | Article |
| id | doaj-art-422d6af8fce747b5a5b83b8a22a39a98 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-422d6af8fce747b5a5b83b8a22a39a982025-08-20T02:37:51ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/13756531375653Generalized Matrix Exponential Solutions to the AKNS HierarchyJian-bing Zhang0Canyuan Gu1Wen-Xiu Ma2School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaSchool of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaDepartment of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USAGeneralized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different kinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy are also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure.http://dx.doi.org/10.1155/2018/1375653 |
| spellingShingle | Jian-bing Zhang Canyuan Gu Wen-Xiu Ma Generalized Matrix Exponential Solutions to the AKNS Hierarchy Advances in Mathematical Physics |
| title | Generalized Matrix Exponential Solutions to the AKNS Hierarchy |
| title_full | Generalized Matrix Exponential Solutions to the AKNS Hierarchy |
| title_fullStr | Generalized Matrix Exponential Solutions to the AKNS Hierarchy |
| title_full_unstemmed | Generalized Matrix Exponential Solutions to the AKNS Hierarchy |
| title_short | Generalized Matrix Exponential Solutions to the AKNS Hierarchy |
| title_sort | generalized matrix exponential solutions to the akns hierarchy |
| url | http://dx.doi.org/10.1155/2018/1375653 |
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