Solutions of some class of nonlinear PDEs in mathematical physics
In this work, the modified simple equation (MSE) method is applied to some class of nonlinear PDEs, namely, a system of nonlinear PDEs, a (2 + 1)-dimensional nonlinear model generated by the Jaulent–Miodek hierarchy, and a generalized KdV equation with two power nonlinearities. As a result, exact tr...
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SpringerOpen
2016-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X15000267 |
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doaj-4b8842cec0f844249104dcb69f1f11152020-11-25T02:37:33ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2016-04-0124221421910.1016/j.joems.2015.02.005Solutions of some class of nonlinear PDEs in mathematical physicsShoukry El-GanainiIn this work, the modified simple equation (MSE) method is applied to some class of nonlinear PDEs, namely, a system of nonlinear PDEs, a (2 + 1)-dimensional nonlinear model generated by the Jaulent–Miodek hierarchy, and a generalized KdV equation with two power nonlinearities. As a result, exact traveling wave solutions involving parameters have been obtained for the considered nonlinear equations in a concise manner. When these parameters are chosen as special values, the solitary wave solutions are derived. It is shown that the proposed technique provides a more powerful mathematical tool for constructing exact solutions for a broad variety of nonlinear PDEs in mathematical physics.http://www.sciencedirect.com/science/article/pii/S1110256X15000267Modified simple equation methodTraveling wave solutionNonlinear partial differential equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shoukry El-Ganaini |
| spellingShingle |
Shoukry El-Ganaini Solutions of some class of nonlinear PDEs in mathematical physics Journal of the Egyptian Mathematical Society Modified simple equation method Traveling wave solution Nonlinear partial differential equation |
| author_facet |
Shoukry El-Ganaini |
| author_sort |
Shoukry El-Ganaini |
| title |
Solutions of some class of nonlinear PDEs in mathematical physics |
| title_short |
Solutions of some class of nonlinear PDEs in mathematical physics |
| title_full |
Solutions of some class of nonlinear PDEs in mathematical physics |
| title_fullStr |
Solutions of some class of nonlinear PDEs in mathematical physics |
| title_full_unstemmed |
Solutions of some class of nonlinear PDEs in mathematical physics |
| title_sort |
solutions of some class of nonlinear pdes in mathematical physics |
| publisher |
SpringerOpen |
| series |
Journal of the Egyptian Mathematical Society |
| issn |
1110-256X |
| publishDate |
2016-04-01 |
| description |
In this work, the modified simple equation (MSE) method is applied to some class of nonlinear PDEs, namely, a system of nonlinear PDEs, a (2 + 1)-dimensional nonlinear model generated by the Jaulent–Miodek hierarchy, and a generalized KdV equation with two power nonlinearities.
As a result, exact traveling wave solutions involving parameters have been obtained for the considered nonlinear equations in a concise manner. When these parameters are chosen as special values, the solitary wave solutions are derived. It is shown that the proposed technique provides a more powerful mathematical tool for constructing exact solutions for a broad variety of nonlinear PDEs in mathematical physics. |
| topic |
Modified simple equation method Traveling wave solution Nonlinear partial differential equation |
| url |
http://www.sciencedirect.com/science/article/pii/S1110256X15000267 |
| work_keys_str_mv |
AT shoukryelganaini solutionsofsomeclassofnonlinearpdesinmathematicalphysics |
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