Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-12-18 DOI:10.3390/fractalfract7120889

M. M. Al-Sawalha, S. Mukhtar, Rasool Shah, A. Ganie, Khaled Moaddy

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引用次数: 0

Abstract

The primary goal of this study is to create and characterise solitary wave solutions for the conformable Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equations (FCBWBKEs), a model that governs shallow water waves. Through wave transformations and the chain rule, the authors used the modified Extended Direct Algebraic Method (mEDAM) for transforming FCBWBKEs into a more manageable Nonlinear Ordinary Differential Equation (NODE). This accomplishment is particularly noteworthy because it surpasses the drawbacks linked to both the Caputo and Riemann–Liouville definitions in complying to the chain rule. The study uses visual representations such as 3D, 2D, and contour graphs to demonstrate the dynamic nature of solitary wave solutions. Furthermore, the investigation of diverse wave phenomena such as kinks, shock waves, periodic waves, and bell-shaped kink waves highlights the range of knowledge obtained in the study of shallow water wave behavior. Overall, this study introduces novel methodologies that produce valuable and consistent results for the problem under consideration.

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分数耦合 Boussinesq-Whitham-Broer-Kaup 方程非线性动力系统中的孤波传播分析

本研究的主要目标是创建并表征控制浅水波浪的模型--保角耦合布西内斯克-维瑟姆-布罗尔-考普方程（FCBWBKEs）的孤波解。通过波浪变换和链式法则，作者使用修正的扩展直接代数法（mEDAM）将 FCBWBKEs 转换为更易于管理的非线性常微分方程（NODE）。这一成果尤其值得注意，因为它超越了卡普托定义和黎曼-黎欧维尔定义在遵守链式规则方面的缺点。研究使用三维、二维和等值线图等可视化表示方法来展示孤波解的动态性质。此外，对各种波现象（如扭结波、冲击波、周期波和钟形扭结波）的研究突出了在浅水波行为研究中获得的知识范围。总之，本研究引入了新颖的方法，为所考虑的问题提供了有价值且一致的结果。

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

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.