Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics
In this work, we study the solitary wave profiles of the fractional-Sharma–Tasso–Olver equation, which is applicable to particle fission and fusion mechanisms in nuclear physics. In numerical and analytical theories, exact solitary wave solutions are of the uttermost importance for such equations. I...
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AIP Publishing LLC
2025-04-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0264311 |
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| author | Li Ming Jan Muhammad David Yaro Usman Younas |
| author_facet | Li Ming Jan Muhammad David Yaro Usman Younas |
| author_sort | Li Ming |
| collection | DOAJ |
| description | In this work, we study the solitary wave profiles of the fractional-Sharma–Tasso–Olver equation, which is applicable to particle fission and fusion mechanisms in nuclear physics. In numerical and analytical theories, exact solitary wave solutions are of the uttermost importance for such equations. Improved analytical methods are essential for a deeper understanding of dynamics, despite their widespread implementation. In this study, we use the advanced analytical techniques known as generalized Arnous method, modified generalized Riccati equation mapping technique, and Riccati extended simple equation approach for securing a variety of solutions. This study marks a significant milestone by applying the prescribed techniques to the proposed equation using truncated M-fractional derivatives and providing a significant contribution to the existing literature. This equation is widely regarded as a model that illustrates the propagation of nonlinear dispersive waves in inhomogeneous media. Using the suitable wave transformation with the fractional-derivative, the governing equation is converted into an ordinary differential equation to get the required solutions. Various types of solutions, such as mixed, dark, singular, bright–dark, bright, complex, and combined solitons, are extracted. Moreover, another important aspect of this study is to discuss the multistability and sensitivity analysis of the studied model by the assistance of the Galilean transformation and perturbation term. The utilized methods have strong computing capacity, which helps them effectively handle the exact solutions with high accuracy in these systems. In addition, we depict 3D and 2D phase portrait graphs with appropriate parameters to illustrate the solution’s behavior. |
| format | Article |
| id | doaj-art-776e8f3dbdfe405da60791092152a02b |
| institution | DOAJ |
| issn | 2158-3226 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj-art-776e8f3dbdfe405da60791092152a02b2025-08-20T03:11:02ZengAIP Publishing LLCAIP Advances2158-32262025-04-01154045017045017-1310.1063/5.0264311Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physicsLi Ming0Jan Muhammad1David Yaro2Usman Younas3Department of Electronic and Information Engineering, Bozhou University, Bozhou, ChinaDepartment of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics and Statistics, Cape Coast Technical University, P.O. Box DL 50, Cape Coast, GhanaDepartment of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaIn this work, we study the solitary wave profiles of the fractional-Sharma–Tasso–Olver equation, which is applicable to particle fission and fusion mechanisms in nuclear physics. In numerical and analytical theories, exact solitary wave solutions are of the uttermost importance for such equations. Improved analytical methods are essential for a deeper understanding of dynamics, despite their widespread implementation. In this study, we use the advanced analytical techniques known as generalized Arnous method, modified generalized Riccati equation mapping technique, and Riccati extended simple equation approach for securing a variety of solutions. This study marks a significant milestone by applying the prescribed techniques to the proposed equation using truncated M-fractional derivatives and providing a significant contribution to the existing literature. This equation is widely regarded as a model that illustrates the propagation of nonlinear dispersive waves in inhomogeneous media. Using the suitable wave transformation with the fractional-derivative, the governing equation is converted into an ordinary differential equation to get the required solutions. Various types of solutions, such as mixed, dark, singular, bright–dark, bright, complex, and combined solitons, are extracted. Moreover, another important aspect of this study is to discuss the multistability and sensitivity analysis of the studied model by the assistance of the Galilean transformation and perturbation term. The utilized methods have strong computing capacity, which helps them effectively handle the exact solutions with high accuracy in these systems. In addition, we depict 3D and 2D phase portrait graphs with appropriate parameters to illustrate the solution’s behavior.http://dx.doi.org/10.1063/5.0264311 |
| spellingShingle | Li Ming Jan Muhammad David Yaro Usman Younas Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics AIP Advances |
| title | Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics |
| title_full | Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics |
| title_fullStr | Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics |
| title_full_unstemmed | Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics |
| title_short | Exploring the multistability, sensitivity, and wave profiles to the fractional Sharma–Tasso–Olver equation in the mathematical physics |
| title_sort | exploring the multistability sensitivity and wave profiles to the fractional sharma tasso olver equation in the mathematical physics |
| url | http://dx.doi.org/10.1063/5.0264311 |
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