New kink-periodic and convex–concave-periodic solutions to the modified regularized long wave equation by means of modified rational trigonometric–hyperbolic functions

IF 2.4 Q2 ENGINEERING, MECHANICAL

Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0307

M. Alquran, Omar Najadat, Mohammed Ali, S. Qureshi

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引用次数: 0

Abstract

Abstract The significance of different types of periodic solutions in nonlinear equations is vital across various practical applications. Our objective in this study was to uncover novel forms of periodic solutions for the modified regularized long wave equation. This particular model holds great importance in the realm of physics as it characterizes the propagation of weak nonlinearity and space-time dispersion waves, encompassing phenomena like nonlinear transverse waves in shallow water, ion-acoustic waves in plasma, and phonon waves in nonlinear crystals. By employing the methodology of modified rational sine-cosine and sinh–cosh functions, we successfully derived new kink-periodic and convex–concave-periodic solutions. To showcase the superiority of our proposed approach, we conducted a comparative analysis with the alternative Kudryashov-expansion technique. Furthermore, we visually depicted the diverse recovery solutions through 2D and 3D plots to enhance the understanding of our findings.

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用修正有理三角双曲函数求解修正正则长波方程的新扭周期解和凸凹周期解

非线性方程中不同类型周期解的意义在各种实际应用中都是至关重要的。本研究的目的是揭示修正正则化长波方程周期解的新形式。这种特殊的模型在物理学领域具有重要意义，因为它表征了弱非线性和时空色散波的传播，包括浅水中的非线性横波，等离子体中的离子声波和非线性晶体中的声子波等现象。利用修正有理正弦余弦函数和sinh-cosh函数的方法，成功地导出了新的扭结周期解和凹凸周期解。为了展示我们提出的方法的优越性，我们与另一种kudryashov展开技术进行了比较分析。此外，我们通过2D和3D图直观地描述了不同的恢复方案，以增强对我们研究结果的理解。

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

Nonlinear Engineering - Modeling and Application Multiple-

CiteScore

6.20

自引率

3.60%

发文量

审稿时长

44 weeks

期刊介绍： The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.