Probing the diversity of soliton phenomena within conformable Estevez-Mansfield-Clarkson equation in shallow water

Mohammad Alqudah; Safyan Mukhtar; Haifa A. Alyousef; Sherif M. E. Ismaeel; S. A. El-Tantawy; Fazal Ghani; Mohammad Alqudah; Safyan Mukhtar; Haifa A. Alyousef; Sherif M. E. Ismaeel; S. A. El-Tantawy; Fazal Ghani

doi:10.3934/math.20241030

AIMS Mathematics

2024, Volume 9, Issue 8: 21212-21238. doi: 10.3934/math.20241030

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Probing the diversity of soliton phenomena within conformable Estevez-Mansfield-Clarkson equation in shallow water

1.
Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, Jordan
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 Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
5.
Department of Physics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
6.
Department of Physics, Faculty of Science, Ain Shams University, Cairo, Egypt
7.
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
8.
Department of Physics, Faculty of Science, Al-Baha University, Al-Baha P.O. Box 1988, Saudi Arabia
9.
Department of mathematics, Abdul Wali Khan University Mardan, Pakistan

Received: 31 January 2024 Revised: 26 May 2024 Accepted: 03 June 2024 Published: 01 July 2024
MSC : 34G20, 35A20, 35A22, 35R11

This study aims to employ the extended direct algebraic method (EDAM) to generate and evaluate soliton solutions to the nonlinear, space-time conformable Estevez Mansfield-Clarkson equation (CEMCE), which is utilized to simulate shallow water waves. The proposed method entails transforming nonlinear fractional partial differential equations (NFPDEs) into nonlinear ordinary differential equations (NODEs) under the assumption of a finite series solution by utilizing Riccati ordinary differential equations. Various mathematical structures/solutions for the current model are derived in the form of rational, exponential, trigonometric, and hyperbolic functions. The wide range of obtained solutions allows for a thorough analysis of their actual wave characteristics. The 3D and 2D graphs are used to illustrate that these behaviors consistently manifest as periodic, dark, and bright kink solitons. Notably, the produced soliton solutions offer new and critical insights into the intricate behaviors of the CEMCE by illuminating the basic mechanics of the wave's interaction and propagation. By analyzing these solutions, academics can better understand the model's behavior in various settings. These solutions shed light on complicated issues such as configuration dispersion in liquid drops and wave behavior in shallow water.
- soliton solutions,
- conformable Estevez-Mansfield-Clarkson equation,
- conformable derivative,
- shallow water,
- extended direct algebraic method
Citation: Mohammad Alqudah, Safyan Mukhtar, Haifa A. Alyousef, Sherif M. E. Ismaeel, S. A. El-Tantawy, Fazal Ghani. Probing the diversity of soliton phenomena within conformable Estevez-Mansfield-Clarkson equation in shallow water[J]. AIMS Mathematics, 2024, 9(8): 21212-21238. doi: 10.3934/math.20241030

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Abstract

This study aims to employ the extended direct algebraic method (EDAM) to generate and evaluate soliton solutions to the nonlinear, space-time conformable Estevez Mansfield-Clarkson equation (CEMCE), which is utilized to simulate shallow water waves. The proposed method entails transforming nonlinear fractional partial differential equations (NFPDEs) into nonlinear ordinary differential equations (NODEs) under the assumption of a finite series solution by utilizing Riccati ordinary differential equations. Various mathematical structures/solutions for the current model are derived in the form of rational, exponential, trigonometric, and hyperbolic functions. The wide range of obtained solutions allows for a thorough analysis of their actual wave characteristics. The 3D and 2D graphs are used to illustrate that these behaviors consistently manifest as periodic, dark, and bright kink solitons. Notably, the produced soliton solutions offer new and critical insights into the intricate behaviors of the CEMCE by illuminating the basic mechanics of the wave's interaction and propagation. By analyzing these solutions, academics can better understand the model's behavior in various settings. These solutions shed light on complicated issues such as configuration dispersion in liquid drops and wave behavior in shallow water.

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