The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations
A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonl...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/960798 |
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| author | Yun-Mei Zhao Ying-Hui He Yao Long |
| author_facet | Yun-Mei Zhao Ying-Hui He Yao Long |
| author_sort | Yun-Mei Zhao |
| collection | DOAJ |
| description | A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system,
the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method. |
| format | Article |
| id | doaj-art-a2ee6f4f83ca4b4badd9995853c614a6 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a2ee6f4f83ca4b4badd9995853c614a62025-08-20T03:38:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/960798960798The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ EquationsYun-Mei Zhao0Ying-Hui He1Yao Long2Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaDepartment of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaDepartment of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaA good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.http://dx.doi.org/10.1155/2013/960798 |
| spellingShingle | Yun-Mei Zhao Ying-Hui He Yao Long The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations Journal of Applied Mathematics |
| title | The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations |
| title_full | The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations |
| title_fullStr | The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations |
| title_full_unstemmed | The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations |
| title_short | The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations |
| title_sort | simplest equation method and its application for solving the nonlinear nlse kgz gds ds and gz equations |
| url | http://dx.doi.org/10.1155/2013/960798 |
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