A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation
In this paper, we use the Riccati–Bernoulli sub-ODE method in conjunction with the Bäcklund transformation to find out the exact solutions of the nonlinear time–space fractional Bogoyavlenskii equation. The obtained solutions encompass multiple kink solitary wave solutions that are quite unique and...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241678 |
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| author | Yousef Jawarneh Humaira Yasmin Ali M. Mahnashi |
| author_facet | Yousef Jawarneh Humaira Yasmin Ali M. Mahnashi |
| author_sort | Yousef Jawarneh |
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| description | In this paper, we use the Riccati–Bernoulli sub-ODE method in conjunction with the Bäcklund transformation to find out the exact solutions of the nonlinear time–space fractional Bogoyavlenskii equation. The obtained solutions encompass multiple kink solitary wave solutions that are quite unique and important in addition to solutions presented in hyperbolic, trigonometric, and rational function forms. This equation describes central factors influencing its behavior including fluid dynamics in shallow water waves and plasma, which demonstrates our conclusions have broad applications for such systems. We also study the effect of the fractional order parameter ($ \alpha $) on solutions and plot their behavior using MATLAB in two dimensions. This work also contributes to the knowledge of the physical structures of the fractional Bogoyavlenskyi equation apart from showcasing the potential of the Riccati–Bernoulli sub-ODE method when applied to nonlinear fractional differential equations. |
| format | Article |
| id | doaj-art-008e62de5035425bb5be862e8dce6272 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-008e62de5035425bb5be862e8dce62722025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912353083532510.3934/math.20241678A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformationYousef Jawarneh0Humaira Yasmin1Ali M. Mahnashi2Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi ArabiaDepartment of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi ArabiaIn this paper, we use the Riccati–Bernoulli sub-ODE method in conjunction with the Bäcklund transformation to find out the exact solutions of the nonlinear time–space fractional Bogoyavlenskii equation. The obtained solutions encompass multiple kink solitary wave solutions that are quite unique and important in addition to solutions presented in hyperbolic, trigonometric, and rational function forms. This equation describes central factors influencing its behavior including fluid dynamics in shallow water waves and plasma, which demonstrates our conclusions have broad applications for such systems. We also study the effect of the fractional order parameter ($ \alpha $) on solutions and plot their behavior using MATLAB in two dimensions. This work also contributes to the knowledge of the physical structures of the fractional Bogoyavlenskyi equation apart from showcasing the potential of the Riccati–Bernoulli sub-ODE method when applied to nonlinear fractional differential equations.https://www.aimspress.com/article/doi/10.3934/math.20241678fractional bogoyavlenskii equationbäcklund transformationnon-linear differential equationsexact solutions |
| spellingShingle | Yousef Jawarneh Humaira Yasmin Ali M. Mahnashi A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation AIMS Mathematics fractional bogoyavlenskii equation bäcklund transformation non-linear differential equations exact solutions |
| title | A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation |
| title_full | A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation |
| title_fullStr | A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation |
| title_full_unstemmed | A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation |
| title_short | A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation |
| title_sort | new solitary wave solution of the fractional phenomena bogoyavlenskii equation via backlund transformation |
| topic | fractional bogoyavlenskii equation bäcklund transformation non-linear differential equations exact solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241678 |
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