Investigation of New Solitary Wave Solutions of the Gilson-Pickering Equation Using Advanced Computational Techniques

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
M. M. Abelazeem, Raghda A. M. Attia
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引用次数: 0

Abstract

This study focuses on employing recent and accurate computational techniques, specifically the Sardar-sub equation [Formula: see text] method, to explore novel solitary wave solutions of the Gilson–Pickering [Formula: see text] equation. The GP equation is a mathematical model with implications in fluid dynamics and wave phenomena. It describes the behavior of solitary waves, which are localized disturbances propagating through a medium without changing shape. The physical significance of the [Formula: see text] equation lies in its ability to capture the dynamics of solitary waves in various systems, including water waves, optical fibers, and nonlinear acoustic waves. The study’s findings contribute to the advancement of mathematical modeling approaches and offer valuable insights into solitary wave phenomena. The stability of the constructed solutions is investigated using the properties of the Hamiltonian system. The accuracy of the computational solutions is demonstrated by comparing them with approximate solutions obtained through He’s variational iteration [Formula: see text] method. Furthermore, the effectiveness of the employed computational techniques is validated through comparisons with other existing methods.
利用先进的计算技术研究Gilson-Pickering方程的新孤波解
本研究的重点是采用最新的精确计算技术,特别是Sardar-sub方程[公式:见文本]方法,探索Gilson-Pickering[公式:见文本]方程的新颖孤波解。GP方程是一个涉及流体力学和波动现象的数学模型。它描述了孤波的行为,孤波是通过介质传播而不改变形状的局部扰动。[公式:见文本]方程的物理意义在于它能够捕捉各种系统中孤波的动力学,包括水波、光纤和非线性声波。这项研究的发现有助于数学建模方法的进步,并为孤立波现象提供了有价值的见解。利用哈密顿系统的性质研究了构造解的稳定性。通过与何氏变分迭代法[公式:见文]近似解的比较,证明了计算解的准确性。此外,通过与其他现有方法的比较,验证了所采用计算技术的有效性。
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
CiteScore
7.20
自引率
4.30%
发文量
567
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