Kink soliton phenomena of fractional conformable Kairat equations
This paper presents a new scientific method to obtain the precise soliton solutions of the fractional conformable Kairat-Ⅱ (K-IIE) and Kairat-X (K-XE) equations using the Riccati-Bernoulli sub-ODE technique and the Bäcklund transformation. These methods seem most effective compared to the previously...
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| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025131 |
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| author | M. Mossa Al-Sawalha Safyan Mukhtar Azzh Saad Alshehry Mohammad Alqudah Musaad S. Aldhabani |
| author_facet | M. Mossa Al-Sawalha Safyan Mukhtar Azzh Saad Alshehry Mohammad Alqudah Musaad S. Aldhabani |
| author_sort | M. Mossa Al-Sawalha |
| collection | DOAJ |
| description | This paper presents a new scientific method to obtain the precise soliton solutions of the fractional conformable Kairat-Ⅱ (K-IIE) and Kairat-X (K-XE) equations using the Riccati-Bernoulli sub-ODE technique and the Bäcklund transformation. These methods seem most effective compared to the previously used methods as they demonstrate novelty in intensity and potential application. The solutions attained in form of trigonometric, hyperbolic, and rational forms can be used in areas of nonlinear optics, ferromagnetic dynamics, photonic crystals, and optical fibers theory. The most important findings are displayed in simple $ 2D $ graphs in order to illustrate the nature of these solutions. The use of the flexible fractional derivatives shows that the models are integrated and provides opportunities for studying differential geometry and curve equivalence. Similarly, the ease of the methods underscores applications in other nonlinear partial differential equations, affirming their versatility and importance for the upper level courses. |
| format | Article |
| id | doaj-art-e5705060566e4d44b8b340f1ad393c34 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e5705060566e4d44b8b340f1ad393c342025-08-20T03:17:09ZengAIMS PressAIMS Mathematics2473-69882025-02-011022808282810.3934/math.2025131Kink soliton phenomena of fractional conformable Kairat equationsM. Mossa Al-Sawalha0Safyan Mukhtar1Azzh Saad Alshehry2Mohammad Alqudah3Musaad S. Aldhabani4Department 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 Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, JordanDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O.Box741, Tabuk 71491, Saudi ArabiaThis paper presents a new scientific method to obtain the precise soliton solutions of the fractional conformable Kairat-Ⅱ (K-IIE) and Kairat-X (K-XE) equations using the Riccati-Bernoulli sub-ODE technique and the Bäcklund transformation. These methods seem most effective compared to the previously used methods as they demonstrate novelty in intensity and potential application. The solutions attained in form of trigonometric, hyperbolic, and rational forms can be used in areas of nonlinear optics, ferromagnetic dynamics, photonic crystals, and optical fibers theory. The most important findings are displayed in simple $ 2D $ graphs in order to illustrate the nature of these solutions. The use of the flexible fractional derivatives shows that the models are integrated and provides opportunities for studying differential geometry and curve equivalence. Similarly, the ease of the methods underscores applications in other nonlinear partial differential equations, affirming their versatility and importance for the upper level courses.https://www.aimspress.com/article/doi/10.3934/math.2025131kairat-ⅱ equation (k-iie)kairat-x equation (k-xe)bäcklund transformationnon-linear differential equationsexact solutions |
| spellingShingle | M. Mossa Al-Sawalha Safyan Mukhtar Azzh Saad Alshehry Mohammad Alqudah Musaad S. Aldhabani Kink soliton phenomena of fractional conformable Kairat equations AIMS Mathematics kairat-ⅱ equation (k-iie) kairat-x equation (k-xe) bäcklund transformation non-linear differential equations exact solutions |
| title | Kink soliton phenomena of fractional conformable Kairat equations |
| title_full | Kink soliton phenomena of fractional conformable Kairat equations |
| title_fullStr | Kink soliton phenomena of fractional conformable Kairat equations |
| title_full_unstemmed | Kink soliton phenomena of fractional conformable Kairat equations |
| title_short | Kink soliton phenomena of fractional conformable Kairat equations |
| title_sort | kink soliton phenomena of fractional conformable kairat equations |
| topic | kairat-ⅱ equation (k-iie) kairat-x equation (k-xe) bäcklund transformation non-linear differential equations exact solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025131 |
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