Analytical Solutions for Nonlinear Dispersive Physical Model
Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are pres...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/3714832 |
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| author | Wen-Xiu Ma Mohamed R. Ali R. Sadat |
| author_facet | Wen-Xiu Ma Mohamed R. Ali R. Sadat |
| author_sort | Wen-Xiu Ma |
| collection | DOAJ |
| description | Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM. |
| format | Article |
| id | doaj-art-f583fbdecde54c7aab3cfb3035769ca6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f583fbdecde54c7aab3cfb3035769ca62025-02-03T05:53:56ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/37148323714832Analytical Solutions for Nonlinear Dispersive Physical ModelWen-Xiu Ma0Mohamed R. Ali1R. Sadat2Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, ChinaDepartment of Basic Science, Faculty of Engineering at Benha, Benha University, 13512, EgyptDepartment of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, EgyptNonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.http://dx.doi.org/10.1155/2020/3714832 |
| spellingShingle | Wen-Xiu Ma Mohamed R. Ali R. Sadat Analytical Solutions for Nonlinear Dispersive Physical Model Complexity |
| title | Analytical Solutions for Nonlinear Dispersive Physical Model |
| title_full | Analytical Solutions for Nonlinear Dispersive Physical Model |
| title_fullStr | Analytical Solutions for Nonlinear Dispersive Physical Model |
| title_full_unstemmed | Analytical Solutions for Nonlinear Dispersive Physical Model |
| title_short | Analytical Solutions for Nonlinear Dispersive Physical Model |
| title_sort | analytical solutions for nonlinear dispersive physical model |
| url | http://dx.doi.org/10.1155/2020/3714832 |
| work_keys_str_mv | AT wenxiuma analyticalsolutionsfornonlineardispersivephysicalmodel AT mohamedrali analyticalsolutionsfornonlineardispersivephysicalmodel AT rsadat analyticalsolutionsfornonlineardispersivephysicalmodel |