New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation
This article was published in the Journal of Applied Mathematics [© 2012 Hasibun Naher and Farah Aini Abdullah.] and the definite version is available at : http://dx.doi.org/10.1155/2012/486458 The Journal's website is at:https://www.hindawi.com/journals/jam/2012/486458/
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© 2012 Journal of Applied Mathematics
2016
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| Linkit: | http://hdl.handle.net/10361/6871 http://dx.doi.org/10.1155/2012/486458 |
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10361-68712016-11-17T07:59:46Z New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation Naher, Hasibun Abdullah, Farah Aini Department of Mathematics and Natural Sciences, BRAC University This article was published in the Journal of Applied Mathematics [© 2012 Hasibun Naher and Farah Aini Abdullah.] and the definite version is available at : http://dx.doi.org/10.1155/2012/486458 The Journal's website is at:https://www.hindawi.com/journals/jam/2012/486458/ The generalized Riccati equation mapping is extended with the basic (G ′ / G) -expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G ′ (η) = w + u G (η) + v G 2 (η) is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple. Published 2016-11-17T07:58:00Z 2016-11-17T07:58:00Z 2012 Article Naher, H., & Abdullah, F. A. (2012). New traveling wave solutions by the extended generalized riccati equation mapping method of the (2 + 1) -dimensional evolution equation. Journal of Applied Mathematics, 2012 doi:10.1155/2012/486458 1110757X http://hdl.handle.net/10361/6871 http://dx.doi.org/10.1155/2012/486458 en https://www.hindawi.com/journals/jam/2012/486458/ © 2012 Journal of Applied Mathematics |
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Brac University |
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Institutional Repository |
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English |
| description |
This article was published in the Journal of Applied Mathematics [© 2012 Hasibun Naher and Farah Aini Abdullah.] and the definite version is available at : http://dx.doi.org/10.1155/2012/486458 The Journal's website is at:https://www.hindawi.com/journals/jam/2012/486458/ |
| author2 |
Department of Mathematics and Natural Sciences, BRAC University |
| author_facet |
Department of Mathematics and Natural Sciences, BRAC University Naher, Hasibun Abdullah, Farah Aini |
| format |
Article |
| author |
Naher, Hasibun Abdullah, Farah Aini |
| spellingShingle |
Naher, Hasibun Abdullah, Farah Aini New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| author_sort |
Naher, Hasibun |
| title |
New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| title_short |
New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| title_full |
New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| title_fullStr |
New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| title_full_unstemmed |
New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| title_sort |
new traveling wave solutions by the extended generalized riccati equation mapping method of the (2 + 1) -dimensional evolution equation |
| publisher |
© 2012 Journal of Applied Mathematics |
| publishDate |
2016 |
| url |
http://hdl.handle.net/10361/6871 http://dx.doi.org/10.1155/2012/486458 |
| work_keys_str_mv |
AT naherhasibun newtravelingwavesolutionsbytheextendedgeneralizedriccatiequationmappingmethodofthe21dimensionalevolutionequation AT abdullahfarahaini newtravelingwavesolutionsbytheextendedgeneralizedriccatiequationmappingmethodofthe21dimensionalevolutionequation |
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1814309756509093888 |