High-accuracy solution for fractional solitary wave dynamics in finite water depth with linear shear flow, wind, and dissipation effects

In this paper, a fractional nonlinear Schrödinger equation has been initially derived for capturing the dynamics of gravity waves in finite water depth, accounting for factors such as wind, dissipation, and shear currents. A comprehensive framework is established to enhance the model's representation of gravity wave behavior. We employ a high-order iterative method, specifically the homotopy iterative technique, along with a non-uniform collocation approach integrated into the Haar wavelet method, resulting in a novel computational method characterized by high precision and efficiency. The robustness and reliability of the proposed approach are validated through convergence analysis and comparisons with analytical solutions. Furthermore, the results indicate that the nonlinear and dispersive effects caused by the fractional orders lead to changes in the propagation characteristics of gravity waves. The impacts of the damping coefficient related to wind action and dissipative effects on the temporal evolution of solitary waves are also discussed. The construction of the fractional model holds far-reaching significance for researching the nonlinear propagation of gravity waves in actual ocean water waves. Additionally, an outstanding computational technique for solving fractional nonlinear evolution equations in diverse applications has been developed.