Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method
The (3 + 1)-dimensional generalized shallow water equation is a significant mathematical framework for analyzing the dynamic behavior of waves in ocean physics. The purpose of this article is to investigate some more generic soliton solutions of the generalized shallow water-like model in three dime...
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| Format: | Article |
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Taylor & Francis Group
2024-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2024.2313245 |
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| author | Pinakee Dey Lamiaa H. Sadek M. M. Tharwat Shuvo Sarker Rezaul Karim M. Ali Akbar Nasser S. Elazab M. S. Osman |
| author_facet | Pinakee Dey Lamiaa H. Sadek M. M. Tharwat Shuvo Sarker Rezaul Karim M. Ali Akbar Nasser S. Elazab M. S. Osman |
| author_sort | Pinakee Dey |
| collection | DOAJ |
| description | The (3 + 1)-dimensional generalized shallow water equation is a significant mathematical framework for analyzing the dynamic behavior of waves in ocean physics. The purpose of this article is to investigate some more generic soliton solutions of the generalized shallow water-like model in three dimensions. The investigation is conducted utilizing the sophisticated mathematical methodology known as the double variables [Formula: see text] expansion technique. With this approach, we produce new propagating wave solutions for this model in the form of hyperbolic, trigonometric, and rational functions. In addition, we offer two- and three-dimensional graphical representations to help visualize the intricate physical phenomena of the system. We have constructed many soliton solutions, such as kink shape soliton solutions, anti-bell shape solutions, single periodic solutions, singular soliton solutions, and anti-kink shape solutions for different values of the free parameters involved in the obtained solutions. These graphical representations are predicated on certain parameter selections, which facilitate the understanding of the complicated general behavior for this model. Through the presentation of new findings in the field of soliton solutions for the aforementioned equation, this paper offers fresh perspectives and highlights hitherto overlooked aspects of this fascinating mathematical challenge. The paper illuminates new results on soliton solutions with different geometrical structures for the given equation, revealing hitherto overlooked facets of this intriguing mathematical challenge. |
| format | Article |
| id | doaj-art-1b2621ca64014e94a9bb1132c5cc1400 |
| institution | DOAJ |
| issn | 2576-5299 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj-art-1b2621ca64014e94a9bb1132c5cc14002025-08-20T02:49:26ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992024-12-0131112113110.1080/25765299.2024.2313245Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion methodPinakee Dey0Lamiaa H. Sadek1M. M. Tharwat2Shuvo Sarker3Rezaul Karim4M. Ali Akbar5Nasser S. Elazab6M. S. Osman7Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail 1902, BangladeshDepartment of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef 62511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef 62511, EgyptDepartment of Mathematics, Mawlana Bhashani Science and Technology University, Tangail 1902, BangladeshDepartment of Mathematics, Mawlana Bhashani Science and Technology University, Tangail 1902, BangladeshDepartment of Applied Mathematics, Rajshahi University, Rajshahi 6205, BangladeshDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptThe (3 + 1)-dimensional generalized shallow water equation is a significant mathematical framework for analyzing the dynamic behavior of waves in ocean physics. The purpose of this article is to investigate some more generic soliton solutions of the generalized shallow water-like model in three dimensions. The investigation is conducted utilizing the sophisticated mathematical methodology known as the double variables [Formula: see text] expansion technique. With this approach, we produce new propagating wave solutions for this model in the form of hyperbolic, trigonometric, and rational functions. In addition, we offer two- and three-dimensional graphical representations to help visualize the intricate physical phenomena of the system. We have constructed many soliton solutions, such as kink shape soliton solutions, anti-bell shape solutions, single periodic solutions, singular soliton solutions, and anti-kink shape solutions for different values of the free parameters involved in the obtained solutions. These graphical representations are predicated on certain parameter selections, which facilitate the understanding of the complicated general behavior for this model. Through the presentation of new findings in the field of soliton solutions for the aforementioned equation, this paper offers fresh perspectives and highlights hitherto overlooked aspects of this fascinating mathematical challenge. The paper illuminates new results on soliton solutions with different geometrical structures for the given equation, revealing hitherto overlooked facets of this intriguing mathematical challenge.https://www.tandfonline.com/doi/10.1080/25765299.2024.2313245The (3 + 1)-dimensional generalized shallow water equationthe double variables expansion methodanalytical wave solutions |
| spellingShingle | Pinakee Dey Lamiaa H. Sadek M. M. Tharwat Shuvo Sarker Rezaul Karim M. Ali Akbar Nasser S. Elazab M. S. Osman Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method Arab Journal of Basic and Applied Sciences The (3 + 1)-dimensional generalized shallow water equation the double variables expansion method analytical wave solutions |
| title | Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method |
| title_full | Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method |
| title_fullStr | Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method |
| title_full_unstemmed | Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method |
| title_short | Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method |
| title_sort | soliton solutions to generalized 3 1 dimensional shallow water like equation using the ϕ ϕ 1 ϕ expansion method |
| topic | The (3 + 1)-dimensional generalized shallow water equation the double variables expansion method analytical wave solutions |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2024.2313245 |
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