用tanh-coth方法求解KdV方程广义尺度不变模拟的行波解

IF 2.4 Q2 ENGINEERING, MECHANICAL

Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0325

Oswaldo González-Gaxiola, Juan Ruiz de Chávez

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引用次数: 0

摘要

摘要本文研究了Korteweg-de Vries方程的广义尺度不变模拟。本文首次采用tanh-coth方法求解该非线性方程的行波解。所考虑的广义方程是著名的Korteweg-de Vries (KdV)方程和最近研究的因变量(SIdV)方程的尺度不变之间的联系。得到的结果显示了该模型的许多解族，表明该方程也与KdV和SIdV共享钟形解，正如其他研究人员先前记录的那样。最后，通过执行符号计算，我们证明了所使用的技术是一种有价值和有效的数学工具，可用于解决跨学科非线性科学中出现的问题。

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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Traveling wave solutions of the generalized scale-invariant analog of the KdV equation by tanh–coth method

Abstract In this work, the generalized scale-invariant analog of the Korteweg–de Vries equation is studied. For the first time, the tanh–coth methodology is used to find traveling wave solutions for this nonlinear equation. The considered generalized equation is a connection between the well-known Korteweg–de Vries (KdV) equation and the recently investigated scale-invariant of the dependent variable (SIdV) equation. The obtained results show many families of solutions for the model, indicating that this equation also shares bell-shaped solutions with KdV and SIdV, as previously documented by other researchers. Finally, by executing the symbolic computation, we demonstrate that the used technique is a valuable and effective mathematical tool that can be used to solve problems that arise in the cross-disciplinary nonlinear sciences.

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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.