Kink soliton phenomena of fractional conformable Kairat equations

M. Mossa Al-Sawalha; Safyan Mukhtar; Azzh Saad Alshehry; Mohammad Alqudah; Musaad S. Aldhabani; M. Mossa Al-Sawalha; Safyan Mukhtar; Azzh Saad Alshehry; Mohammad Alqudah; Musaad S. Aldhabani

doi:10.3934/math.2025131

AIMS Mathematics

2025, Volume 10, Issue 2: 2808-2828. doi: 10.3934/math.2025131

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Kink soliton phenomena of fractional conformable Kairat equations

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
4.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
5.
Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, Jordan
6.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box741, Tabuk 71491, Saudi Arabia

Received: 18 September 2024 Revised: 11 January 2025 Accepted: 20 January 2025 Published: 14 February 2025
MSC : 34G20, 35A20, 35A22, 35R11

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.
- Kairat-Ⅱ equation (K-IIE),
- Kairat-X equation (K-XE),
- Bäcklund transformation,
- non-linear differential equations,
- exact solutions
Citation: M. Mossa Al-Sawalha, Safyan Mukhtar, Azzh Saad Alshehry, Mohammad Alqudah, Musaad S. Aldhabani. Kink soliton phenomena of fractional conformable Kairat equations[J]. AIMS Mathematics, 2025, 10(2): 2808-2828. doi: 10.3934/math.2025131

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Abstract

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.

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