Localized Wave and Other Special Wave Solutions to the (3 + 1)-dimensional Kudryashov–Sinelshchikov Equation

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-14 DOI:10.1002/mma.10764

Kang-Jia Wang, Shuai Li, Guo-Dong Wang, Peng Xu, Feng Shi, Xiao-Lian Liu

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引用次数: 0

Abstract

This paper aims to explore some different localized wave solutions to the (3 + 1)-dimensional Kudryashov–Sinelshchikov equation (KSe) for the liquid with gas bubbles. First, the traveling wave transformation is employed to reduce the dimension of the (3 + 1)-dimensional KSe. Then the Hirota bilinear method is adopted to develop the rogue wave solutions via introducing the different polynomial functions. By optimizing the parameters, the bright and dark rogue waves solutions of the first-order and second-order are extracted. In addition, the three-wave method is employed to seek the generalized breathers wave, W-shape (double well or breather wave), bright and dark solitary wave solutions. Besides, the other special wave solutions like the compacton and singular wave solutions are also reported. Meanwhile, the dynamic attributes of some solutions are unfolded by Maple. To the best of the authors' knowledge, the findings of this research are all new and have not explored in other literature.

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（3 + 1）维Kudryashov-Sinelshchikov方程的局域波和其他特殊波解

本文旨在探讨含气泡液体的（3 + 1）维Kudryashov-Sinelshchikov方程（KSe）的几种不同局域波解。首先，采用行波变换对（3 + 1）维KSe进行降维处理。然后通过引入不同的多项式函数，采用Hirota双线性方法展开了异常波解。通过优化参数，提取了一阶和二阶亮、暗异常波解。此外，采用三波法寻求广义呼吸波、w型（双井或呼吸波）、亮孤立波和暗孤立波解。此外，还报道了其他特殊的波解，如压缩波解和奇异波解。同时，利用Maple展开了部分解的动态属性。据作者所知，这项研究的发现都是新的，没有在其他文献中探讨过。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.