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

IF 5.9 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Ain Shams Engineering Journal Pub Date : 2025-09-01 DOI:10.1016/j.asej.2025.103700

Tianyong Han , Yueyong Jiang , Hongguang Fan

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引用次数: 0

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.

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探索浅水波浪现象：whitham - broer - kap - boussinesq - kupershmidt系统的分数方法

本研究利用适形导数将whitham - broer - kop - boussinesq - kupershmidt （WBKBK）系统推广为分数阶模型，旨在更好地捕捉浅水波中的波耗散、异常色散和记忆效应。利用改进的扩展直接代数方法（MEDAM）导出了一系列孤立波解，包括扭结波、周期波和孤子。利用四次b样条配点法进行了数值模拟，验证了解析结果与数值结果的一致性。一个典型扭结波解的线性稳定性分析说明了在特定参数条件下所导出的解的鲁棒性。该研究丰富了分数阶WBKBK系统的理论认识，为流体力学、等离子体物理和非线性光学等领域的复杂波浪动力学建模提供了有价值的工具，在海岸工程和海洋资源开发中具有潜在的应用前景。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ain Shams Engineering Journal Engineering-General Engineering

CiteScore

10.80

自引率

13.30%

发文量

441

审稿时长

49 weeks

期刊介绍： in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance. Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.