Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations
The Sine-Gordon expansion (SGE) method is used to develop exact traveling wave solutions of a family of 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations. The governing equations are reduced to standard ordinary differential equations via companionable wave transformation. The order of the...
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| Language: | English |
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Elsevier
2022-09-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722004934 |
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| author | Abdulla-Al- Mamun Samsun Nahar Ananna Tianqing An Md. Asaduzzaman Md. Sohel Rana |
| author_facet | Abdulla-Al- Mamun Samsun Nahar Ananna Tianqing An Md. Asaduzzaman Md. Sohel Rana |
| author_sort | Abdulla-Al- Mamun |
| collection | DOAJ |
| description | The Sine-Gordon expansion (SGE) method is used to develop exact traveling wave solutions of a family of 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations. The governing equations are reduced to standard ordinary differential equations via companionable wave transformation. The order of the projected polynomial-type solution is figured out using the homogeneous stability approach based on the renowned Sine-Gordon equation. This solution's replacement corresponds to the earlier stage. A system of algebraic equations (SAE) is formed by comparing the coefficients of the powers of the projected solution. A robust coefficient scheme supplies the necessary relationships between parameters and coefficients to develop solutions. Some solutions are modeled for various parameter combinations. Several hyperbolic function solutions are created using the mentioned method. The MATLAB program displays the answers' graphical exemplifications in three-dimensional (3D) surface plots, contour plots, and 2D line plots. The resulting solutions to the equation, with the appropriate parameters, are used to depict the absolute wave configurations in all displays. Additionally, it can conclude that the discovered solutions and their physical characteristics could aid in understanding how shallow water waves propagate in nonlinear dynamics. |
| first_indexed | 2024-12-10T18:43:52Z |
| format | Article |
| id | doaj.art-6e5e551a479540adba84f3b97f7052d0 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-10T18:43:52Z |
| publishDate | 2022-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-6e5e551a479540adba84f3b97f7052d02022-12-22T01:37:34ZengElsevierResults in Physics2211-37972022-09-0140105845Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equationsAbdulla-Al- Mamun0Samsun Nahar Ananna1Tianqing An2Md. Asaduzzaman3Md. Sohel Rana4Department of Mathematics, College of Science, Hohai University, Nanjing 210098, PR China; Department of Computer Science and Engineering, Northern University of Business and Technology Khulna, Khulna 9100, Bangladesh; Corresponding author at: Lecturer in Mathematics, Department of Computer Science and Engineering, Northern University of Business and Technology Khulna, Khulna 9100, Bangladesh; Mobile: +8801741183886.Department of Mathematics, College of Science, Hohai University, Nanjing 210098, PR ChinaDepartment of Mathematics, College of Science, Hohai University, Nanjing 210098, PR ChinaDepartment of Mathematics, Islamic University, Kushtia 7003, BangladeshDepartment of Electrical and Electronic Engineering, Northern University of Business and Technology Khulna, Khulna 9100, BangladeshThe Sine-Gordon expansion (SGE) method is used to develop exact traveling wave solutions of a family of 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations. The governing equations are reduced to standard ordinary differential equations via companionable wave transformation. The order of the projected polynomial-type solution is figured out using the homogeneous stability approach based on the renowned Sine-Gordon equation. This solution's replacement corresponds to the earlier stage. A system of algebraic equations (SAE) is formed by comparing the coefficients of the powers of the projected solution. A robust coefficient scheme supplies the necessary relationships between parameters and coefficients to develop solutions. Some solutions are modeled for various parameter combinations. Several hyperbolic function solutions are created using the mentioned method. The MATLAB program displays the answers' graphical exemplifications in three-dimensional (3D) surface plots, contour plots, and 2D line plots. The resulting solutions to the equation, with the appropriate parameters, are used to depict the absolute wave configurations in all displays. Additionally, it can conclude that the discovered solutions and their physical characteristics could aid in understanding how shallow water waves propagate in nonlinear dynamics.http://www.sciencedirect.com/science/article/pii/S2211379722004934The sine-Gordon expansion methodWazwaz-Benjamin-Bona-Mahony equationSolitary waveExact solutionLump shapeSoliton shape |
| spellingShingle | Abdulla-Al- Mamun Samsun Nahar Ananna Tianqing An Md. Asaduzzaman Md. Sohel Rana Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations Results in Physics The sine-Gordon expansion method Wazwaz-Benjamin-Bona-Mahony equation Solitary wave Exact solution Lump shape Soliton shape |
| title | Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations |
| title_full | Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations |
| title_fullStr | Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations |
| title_full_unstemmed | Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations |
| title_short | Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations |
| title_sort | sine gordon expansion method to construct the solitary wave solutions of a family of 3d fractional wbbm equations |
| topic | The sine-Gordon expansion method Wazwaz-Benjamin-Bona-Mahony equation Solitary wave Exact solution Lump shape Soliton shape |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722004934 |
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