Work

Exploring shallow water wave phenomena: A fractional approach to the Whitham-Broer-Kaup-Boussinesq-Kupershmidt system

Year: 2025

Type: article

Abstract: This study generalizes the Whitham-Broer-Kaup-Boussinesq-Kupershmidt (WBKBK) system to a fractional-order model using conformable derivatives, aiming to better capture wave dissipation, anomalous dispersion, and memory effects in shallow water waves. The Modified Extended Direct Algebraic Method (MEDAM) is employed to derive a series of solitary wave solutions, including kink waves, periodic waves, and solitons. These solutions are validated through numerical simulations using the quartic B-spline collocation method, demonstrating excellent agreement between analytical and numerical results. A linear stability analysis of a representative kink wave solution illustrates the robustness of the derived solutions under specific parameter conditions. This research enriches the theoretical understanding of fractional WBKBK systems and provides valuable tools for modeling complex wave dynamics in fluid dynamics, plasma physics, and nonlinear optics, with potential applications in coastal engineering and marine resource development.

Source: Ain Shams Engineering Journal

DOI: 10.1016/j.asej.2025.103700

Authors: Tianyong Han, Yueyong Jiang, Hongguang Fan

Institutions: Mianyang Normal University, Chengdu University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: Chengdu University, Sichuan Province Science and Technology Support Program