Abundant Solitary Solutions for the Fractional Unidirectional Wave Model Using in Oceanography, Coastal engineering, and Meteorology

Authors

  • Wael Mohammed Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
  • M. W. Alshammary Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
  • Ahmed E. Matouk Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
  • Naveed Iqbal Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6422

Keywords:

beta-derivative, F-expansion method, Exact solutions, nonlinear evolution equations

Abstract

In this paper, we consider the unidirectional wave model (UWM) with beta-derivative operator (BDO). This model simplifies the complexity of wave interactions by providing a one-dimensional approach to understanding wave behavior, particularly under conditions where wave directionality plays a crucial role. Its applications are vital in various fields, including oceanography, coastal engineering, and environmental science, contributing significantly to our understanding of wave dynamics and their impact on coastal and marine environments. Therefore, it is crucial to find the solutions for this model. By applying the F-expansion method, we can obtain abundant solutions, including periodic, bright, kink, anti-kink, singular, and dark-bright solitons. Furthermore, the graphs of the solutions are displayed using the MATLAB software to demonstrate how the beta-derivative operator affects the obtained solution.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Physics

License

Copyright (c) 2025 Wael Mohammed, M. W. Alshammary, Ahmed E. Matouk, Naveed Iqbal

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How to Cite

Abundant Solitary Solutions for the Fractional Unidirectional Wave Model Using in Oceanography, Coastal engineering, and Meteorology. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6422. https://doi.org/10.29020/nybg.ejpam.v18i3.6422