Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method
In this paper, we demonstrate the effectiveness of the new generalized (G′/G)-expansion method by seeking more exact solutions via the mKdV equation and the Gardner equations. The method is direct, concise and simple to implement compared to other existing methods. The traveling wave solutions obtai...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2014-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X14000030 |
| _version_ | 1818217922616623104 |
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| author | Md. Nur Alam M. Ali Akbar |
| author_facet | Md. Nur Alam M. Ali Akbar |
| author_sort | Md. Nur Alam |
| collection | DOAJ |
| description | In this paper, we demonstrate the effectiveness of the new generalized (G′/G)-expansion method by seeking more exact solutions via the mKdV equation and the Gardner equations. The method is direct, concise and simple to implement compared to other existing methods. The traveling wave solutions obtained by this method are expressed in terms of hyperbolic, trigonometric and rational functions. The method shows a wide application for handling nonlinear wave equations. Moreover, the method reduces the large amount of calculations. |
| first_indexed | 2024-12-12T07:15:34Z |
| format | Article |
| id | doaj.art-fa43a32fa55848afbd0b987cdf863e05 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-12T07:15:34Z |
| publishDate | 2014-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-fa43a32fa55848afbd0b987cdf863e052022-12-22T00:33:31ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2014-10-0122340240610.1016/j.joems.2014.01.001Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion methodMd. Nur Alam0M. Ali Akbar1Department of Mathematics, Pabna University of Science and Technology, BangladeshDepartment of Applied Mathematics, University of Rajshahi, BangladeshIn this paper, we demonstrate the effectiveness of the new generalized (G′/G)-expansion method by seeking more exact solutions via the mKdV equation and the Gardner equations. The method is direct, concise and simple to implement compared to other existing methods. The traveling wave solutions obtained by this method are expressed in terms of hyperbolic, trigonometric and rational functions. The method shows a wide application for handling nonlinear wave equations. Moreover, the method reduces the large amount of calculations.http://www.sciencedirect.com/science/article/pii/S1110256X14000030New generalized (G′/G)-expansion methodmKdV equationGardner equationTraveling wave solutionsSolitary wave solutions |
| spellingShingle | Md. Nur Alam M. Ali Akbar Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method Journal of the Egyptian Mathematical Society New generalized (G′/G)-expansion method mKdV equation Gardner equation Traveling wave solutions Solitary wave solutions |
| title | Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method |
| title_full | Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method |
| title_fullStr | Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method |
| title_full_unstemmed | Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method |
| title_short | Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method |
| title_sort | traveling wave solutions for the mkdv equation and the gardner equations by new approach of the generalized g g expansion method |
| topic | New generalized (G′/G)-expansion method mKdV equation Gardner equation Traveling wave solutions Solitary wave solutions |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X14000030 |
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