Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model
In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method). From the point of view...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/1085 |
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| author | Wu Li Lanre Akinyemi Dianchen Lu Mostafa M. A. Khater |
| author_facet | Wu Li Lanre Akinyemi Dianchen Lu Mostafa M. A. Khater |
| author_sort | Wu Li |
| collection | DOAJ |
| description | In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method). From the point of view of group theory, the proposed analytical methods in our article are based on symmetry, and effectively solve those problems which actually possess explicit or implicit symmetry. This model is a vital model in shallow water phenomena where it demonstrates the wave surface propagating in both directions. The obtained analytical solutions are explained by plotting them through 3D, 2D, and contour sketches. These solutions’ accuracy is also tested by calculating the absolute error between them and evaluated numerical results by the Adomian decomposition (AD) method and variational iteration (VI) method. The considered numerical schemes were applied based on constructed initial and boundary conditions through the obtained analytical solutions via the MDA, and MK methods which show the synchronization between computational and numerical obtained solutions. This coincidence between the obtained solutions is explained through two-dimensional and distribution plots. The applied methods’ symmetry is shown through comparing their obtained results and showing the matching between both obtained solutions (analytical and numerical). |
| first_indexed | 2024-03-10T10:18:48Z |
| format | Article |
| id | doaj.art-c3f082940f3b45d49c5b961364324514 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:18:48Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c3f082940f3b45d49c5b9613643245142023-11-22T00:36:00ZengMDPI AGSymmetry2073-89942021-06-01136108510.3390/sym13061085Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves ModelWu Li0Lanre Akinyemi1Dianchen Lu2Mostafa M. A. Khater3Department of Mathematical and Physics, Nanjing Institute of Technology, Nanjing 211167, ChinaDepartment of Mathematics, Prairie View A & M University, Prairie View, TX 77446, USADepartment of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang 212013, ChinaDepartment of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang 212013, ChinaIn this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method). From the point of view of group theory, the proposed analytical methods in our article are based on symmetry, and effectively solve those problems which actually possess explicit or implicit symmetry. This model is a vital model in shallow water phenomena where it demonstrates the wave surface propagating in both directions. The obtained analytical solutions are explained by plotting them through 3D, 2D, and contour sketches. These solutions’ accuracy is also tested by calculating the absolute error between them and evaluated numerical results by the Adomian decomposition (AD) method and variational iteration (VI) method. The considered numerical schemes were applied based on constructed initial and boundary conditions through the obtained analytical solutions via the MDA, and MK methods which show the synchronization between computational and numerical obtained solutions. This coincidence between the obtained solutions is explained through two-dimensional and distribution plots. The applied methods’ symmetry is shown through comparing their obtained results and showing the matching between both obtained solutions (analytical and numerical).https://www.mdpi.com/2073-8994/13/6/1085(2 + 1)-D KP-BBM equationcomputational and numerical simulations |
| spellingShingle | Wu Li Lanre Akinyemi Dianchen Lu Mostafa M. A. Khater Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model Symmetry (2 + 1)-D KP-BBM equation computational and numerical simulations |
| title | Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model |
| title_full | Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model |
| title_fullStr | Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model |
| title_full_unstemmed | Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model |
| title_short | Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model |
| title_sort | abundant traveling wave and numerical solutions of weakly dispersive long waves model |
| topic | (2 + 1)-D KP-BBM equation computational and numerical simulations |
| url | https://www.mdpi.com/2073-8994/13/6/1085 |
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