Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method
In this article, the functional variable method (fvm for short) is introduced to establish new exact travelling solutions of the combined KdV–mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is strai...
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Taylor & Francis Group
2016-12-01
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| Series: | Cogent Mathematics |
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| Online Access: | http://dx.doi.org/10.1080/23311835.2016.1218405 |
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doaj-7ffd587b4ea74548b5e2598a15f8b85e2020-11-25T01:30:55ZengTaylor & Francis GroupCogent Mathematics2331-18352016-12-013110.1080/23311835.2016.12184051218405Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable methodW. Djoudi0A. Zerarka1University Med KhiderUniversity Med KhiderIn this article, the functional variable method (fvm for short) is introduced to establish new exact travelling solutions of the combined KdV–mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is straightforward and concise for several kinds of nonlinear problems. Many new exact travelling wave solutions are successfully obtained.http://dx.doi.org/10.1080/23311835.2016.1218405nonlinear solitontravelling wave solutionsfunctional variablehomogeneous balanceKdV–mKdV |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
W. Djoudi A. Zerarka |
| spellingShingle |
W. Djoudi A. Zerarka Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method Cogent Mathematics nonlinear soliton travelling wave solutions functional variable homogeneous balance KdV–mKdV |
| author_facet |
W. Djoudi A. Zerarka |
| author_sort |
W. Djoudi |
| title |
Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method |
| title_short |
Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method |
| title_full |
Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method |
| title_fullStr |
Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method |
| title_full_unstemmed |
Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method |
| title_sort |
exact solutions for the kdv–mkdv equation with time-dependent coefficients using the modified functional variable method |
| publisher |
Taylor & Francis Group |
| series |
Cogent Mathematics |
| issn |
2331-1835 |
| publishDate |
2016-12-01 |
| description |
In this article, the functional variable method (fvm for short) is introduced to establish new exact travelling solutions of the combined KdV–mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is straightforward and concise for several kinds of nonlinear problems. Many new exact travelling wave solutions are successfully obtained. |
| topic |
nonlinear soliton travelling wave solutions functional variable homogeneous balance KdV–mKdV |
| url |
http://dx.doi.org/10.1080/23311835.2016.1218405 |
| work_keys_str_mv |
AT wdjoudi exactsolutionsforthekdvmkdvequationwithtimedependentcoefficientsusingthemodifiedfunctionalvariablemethod AT azerarka exactsolutionsforthekdvmkdvequationwithtimedependentcoefficientsusingthemodifiedfunctionalvariablemethod |
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