Abundant Solitary Solutions for the Fractional Unidirectional Wave Model Using in Oceanography, Coastal engineering, and Meteorology (European Journal of Pure and Applied Mathematics, 2025)
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.