Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method
Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. This phenomenon is observed in oceanographic research involving sea surface and internal waves...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241593 |
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| author | Wafaa B. Rabie Hamdy M. Ahmed Taher A. Nofal E. M. Mohamed |
| author_facet | Wafaa B. Rabie Hamdy M. Ahmed Taher A. Nofal E. M. Mohamed |
| author_sort | Wafaa B. Rabie |
| collection | DOAJ |
| description | Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. This phenomenon is observed in oceanographic research involving sea surface and internal waves, where intricate multi-dimensional interactions play a crucial role. In this work, we use the improved modified extended tanh function method for the first time to extract the exact solutions of the eighth-order (3+1)-dimensional Kac-Wakimoto equation, which describes the dynamics of fields and the structure of solutions in various physical and mathematical contexts. The proposed method is simple and quick to execute, and it offers more innovative solutions than other methods. As a consequence, through the donation of suitable assumptions for the parameters, some new solutions for dark and singular soliton, as well as Jacobi elliptic, exponential, hyperbolic, and singular periodic forms, are developed. Furthermore, to enhance understanding, graphical representations of certain solutions are included. |
| format | Article |
| id | doaj-art-3a05d3344330444da0b7ec3e871b89c5 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-3a05d3344330444da0b7ec3e871b89c52025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912333863340010.3934/math.20241593Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function methodWafaa B. Rabie0Hamdy M. Ahmed1Taher A. Nofal2E. M. Mohamed3Department of Engineering Mathematics and Physics, Higher Institute of Engineering and Technology, Tanta, EgyptDepartment of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, EgyptDepartment of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaBasic Science Department, Delta Higher Institute for Engineering and Technology, EgyptHigher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. This phenomenon is observed in oceanographic research involving sea surface and internal waves, where intricate multi-dimensional interactions play a crucial role. In this work, we use the improved modified extended tanh function method for the first time to extract the exact solutions of the eighth-order (3+1)-dimensional Kac-Wakimoto equation, which describes the dynamics of fields and the structure of solutions in various physical and mathematical contexts. The proposed method is simple and quick to execute, and it offers more innovative solutions than other methods. As a consequence, through the donation of suitable assumptions for the parameters, some new solutions for dark and singular soliton, as well as Jacobi elliptic, exponential, hyperbolic, and singular periodic forms, are developed. Furthermore, to enhance understanding, graphical representations of certain solutions are included.https://www.aimspress.com/article/doi/10.3934/math.20241593kac-wakimoto equationsoliton solutionshyperbolic solutionswave profile |
| spellingShingle | Wafaa B. Rabie Hamdy M. Ahmed Taher A. Nofal E. M. Mohamed Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method AIMS Mathematics kac-wakimoto equation soliton solutions hyperbolic solutions wave profile |
| title | Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method |
| title_full | Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method |
| title_fullStr | Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method |
| title_full_unstemmed | Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method |
| title_short | Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method |
| title_sort | novel analytical superposed nonlinear wave structures for the eighth order 3 1 dimensional kac wakimoto equation using improved modified extended tanh function method |
| topic | kac-wakimoto equation soliton solutions hyperbolic solutions wave profile |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241593 |
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