Multiple Soliton Solutions, Soliton-Type Solutions and Hyperbolic Solutions for the Benjamin–Bona–Mahony Equation with Variable Coefficients in Rotating Fluids and One-Dimensional Transmitted Waves

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-08-01 DOI:10.1515/ijnsns-2015-0122

Zhi-Fang Zeng, Jian‐Guo Liu

引用次数: 1

Abstract

Abstract With the help of symbolic computation, the Benjamin–Bona–Mahony (BBM) equation with variable coefficients is presented, which was proposed for the first time by Benjamin as the regularized long-wave equation and originally derived as approximation for surface water waves in a uniform channel. By employing the improved (G′/G)$(G^' /G)$-expansion method, the truncated Painlevé expansion method, we derive new auto-Bäcklund transformation, hyperbolic solutions, a variety of traveling wave solutions, soliton-type solutions and two solitary wave solutions of the BBM equation. These obtained solutions possess abundant structures. The figures corresponding to these solutions are illustrated to show the particular localized excitations and the interactions between two solitary waves.

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旋转流体和一维透射波中变系数Benjamin-Bona-Mahony方程的多孤子解、孤子型解和双曲解

摘要利用符号计算的方法，提出了Benjamin - bona - mahony (BBM)变系数方程，该方程由Benjamin首次提出为正则化长波方程，最初是作为均匀通道表面水波的近似推导而来。利用改进的(G ' /G)$(G^' /G)$-展开法和截断painlevel展开法，导出了BBM方程的新的auto-Bäcklund变换、双曲解、各种行波解、孤子型解和两个孤波解。这些解具有丰富的结构。与这些解相对应的图显示了特定的局域激励和两个孤立波之间的相互作用。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.