Breather patterns and other soliton dynamics in (2+1)-dimensional conformable Broer-Kaup-Kupershmit system

Mohammad Alqudah; Safyan Mukhtar; Albandari W. Alrowaily; Sherif. M. E. Ismaeel; S. A. El-Tantawy; Fazal Ghani; Mohammad Alqudah; Safyan Mukhtar; Albandari W. Alrowaily; Sherif. M. E. Ismaeel; S. A. El-Tantawy; Fazal Ghani

doi:10.3934/math.2024669

AIMS Mathematics

2024, Volume 9, Issue 6: 13712-13749. doi: 10.3934/math.2024669

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Breather patterns and other soliton dynamics in (2+1)-dimensional conformable Broer-Kaup-Kupershmit system

1.
Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman, 11180, Jordan
2.
Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, 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 11566, Egypt
7.
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
8.
Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al-Baha 1988, Saudi Arabia
9.
Department of mathematics, Abdul Wali Khan University Mardan, Pakistan

Received: 31 January 2024 Revised: 17 March 2024 Accepted: 27 March 2024 Published: 15 April 2024

In this work, the Extended Direct Algebraic Method (EDAM) is utilized to analyze and solve the fractional (2+1)-dimensional Conformable Broer-Kaup-Kupershmit System (CBKKS) and investigate different types of traveling wave solutions and study the soliton like-solutions. Using the suggested method, the fractional nonlinear partial differential equation (FNPDE) is primarily reduced to an integer-order nonlinear ordinary differential equation (NODE) under the traveling wave transformation, yielding an algebraic system of nonlinear equations. The ensuing algebraic systems are then solved to construct some families of soliton-like solutions and many other physical solutions. Some derived solutions are numerically analyzed using suitable values for the related parameters. The discovered soliton solutions grasp vital importance in fluid mechanics as they offer significant insight into the nonlinear behavior of the targeted model, opening the way for a deeper comprehension of complex physical phenomena and offering valuable applications in the associated areas.
Citation: Mohammad Alqudah, Safyan Mukhtar, Albandari W. Alrowaily, Sherif. M. E. Ismaeel, S. A. El-Tantawy, Fazal Ghani. Breather patterns and other soliton dynamics in (2+1)-dimensional conformable Broer-Kaup-Kupershmit system[J]. AIMS Mathematics, 2024, 9(6): 13712-13749. doi: 10.3934/math.2024669

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Abstract

In this work, the Extended Direct Algebraic Method (EDAM) is utilized to analyze and solve the fractional (2+1)-dimensional Conformable Broer-Kaup-Kupershmit System (CBKKS) and investigate different types of traveling wave solutions and study the soliton like-solutions. Using the suggested method, the fractional nonlinear partial differential equation (FNPDE) is primarily reduced to an integer-order nonlinear ordinary differential equation (NODE) under the traveling wave transformation, yielding an algebraic system of nonlinear equations. The ensuing algebraic systems are then solved to construct some families of soliton-like solutions and many other physical solutions. Some derived solutions are numerically analyzed using suitable values for the related parameters. The discovered soliton solutions grasp vital importance in fluid mechanics as they offer significant insight into the nonlinear behavior of the targeted model, opening the way for a deeper comprehension of complex physical phenomena and offering valuable applications in the associated areas.

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