一类四阶非线性偏微分方程的行波结构

IF 13 1区 工程技术 Q1 ENGINEERING, MARINE Journal of Ocean Engineering and Science Pub Date : 2023-03-01 DOI:10.1016/j.joes.2021.12.006
Handenur Esen , Neslihan Ozdemir , Aydin Secer , Mustafa Bayram
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引用次数: 7

摘要

本文利用Riccati-Bernoulli子常微分方程组方法,给出了两个四阶非线性偏微分方程的一大类行波解。在这种方法中,利用Riccati-Bernoulli方程的行波变换,可以将四阶方程转化为一组代数方程。通过求解代数方程组,我们得到了本文提出的可积四阶方程的新的精确解。通过精确解对非线性模型进行了详细的物理解释,证明了该方法的有效性。Bäcklund变换可以产生给定的两个四阶非线性偏微分方程的无限序列解。最后,通过适当的参数值,给出了本文中一些导出解的三维图。
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Traveling wave structures of some fourth-order nonlinear partial differential equations

This study presents a large family of the traveling wave solutions to the two fourth-order nonlinear partial differential equations utilizing the Riccati-Bernoulli sub-ODE method. In this method, utilizing a traveling wave transformation with the aid of the Riccati-Bernoulli equation, the fourth-order equation can be transformed into a set of algebraic equations. Solving the set of algebraic equations, we acquire the novel exact solutions of the integrable fourth-order equations presented in this research paper. The physical interpretation of the nonlinear models are also detailed through the exact solutions, which demonstrate the effectiveness of the presented method.The Bäcklund transformation can produce an infinite sequence of solutions of the given two fourth-order nonlinear partial differential equations. Finally, 3D graphs of some derived solutions in this paper are depicted through suitable parameter values.

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来源期刊
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.
期刊最新文献
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