Characterizing shallow water waves in channels with variable width and depth; computational and numerical simulations

Abstract

This study investigates novel solutions to the fractional Caudrey–Dodd–Gibbon (FCDG) equation, which is a nonlinear partial differential equation that models shallow water waves in channels with varying width and depth. The research employs two computational simulations, namely the Bernoulli sub-equation (BSE) function and extended Khater (EKHA) methods, to analyze the FCDG equation and obtain analytical solutions. The obtained solutions are presented graphically and discussed in various styles, including hyperbolic, rational, and trigonometric formats. The study also examines the strengths and limitations of each method and presents case studies simulating different scenarios, such as wave breaking, run-up, and tsunami propagation. The importance of validation and verification using experimental data or analytical solutions is emphasized to ensure the reliability of numerical solutions. Moreover, the potential impact of computational simulations in predicting real-world shallow water wave behavior, particularly in coastal hazards and ocean engineering, is discussed. This study highlights the usefulness of analytical and numerical techniques in accurately predicting complex phenomena.