Abundant closed-form wave solutions to the simplified modified Camassa-Holm equation

IF 13 1区工程技术 Q1 ENGINEERING, MARINE

Journal of Ocean Engineering and Science Pub Date : 2023-06-01 DOI:10.1016/j.joes.2022.01.012

S M Rayhanul Islam , S M Yiasir Arafat , Hanfeng Wang

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引用次数: 11

Abstract

The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel analytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been extensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenomena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.

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简化修正Camassa-Holm方程的丰富闭式波解

简化修正Camassa-Holm (SMCH)方程是海洋工程和科学中识别各种波浪现象的重要非线性模型方程。将新的辅助方程(NAE)方法应用于SMCH方程。在此基础上，我们得到了SMCH方程的一些新的解析解，如双曲解、三角解、指数解和有理函数解。根据适当的参数值，用Mathematica软件设计三维(3D)和二维(2D)图形。本文还讨论了模型的稳定性问题。这些图广泛地讨论了SMCH方程解的动力学和物理行为。我们所有的解对于理解色散波的非线性现象是必不可少的，这在海洋工程和科学中是重要的。此外，我们的结果对于阐明各种海洋学应用至关重要，这些应用包括海洋重力波、海上钻井平台、与移动海浪相关的能量以及许多其他相关现象。最后，所得解有助于研究许多新结构和高维模型中的波相互作用。

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

Journal of Ocean Engineering and Science Multiple-

CiteScore

11.50

自引率

19.70%

发文量

224

审稿时长

29 days

期刊介绍： The Journal of Ocean Engineering and Science (JOES) serves as a platform for disseminating original research and advancements in the realm of ocean engineering and science. JOES encourages the submission of papers covering various aspects of ocean engineering and science.