Lie Symmetries and Exact Solutions of Shallow Water Equations with Variable Bottom

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2015-12-01 DOI:10.1515/ijnsns-2015-0093

M. Pandey

引用次数: 16

Abstract

Abstract In the present paper, Lie symmetries of nonlinear shallow water equations with variable shapes of the bottom that include horizontal, inclined plane and a parabolic bottom are obtained. Exact particular solutions of the governing system are then obtained using the invariance of the system under these symmetries using Lie’s method. The evolutionary behaviour of the C1$${C^1}$$ discontinuity wave, influenced by the amplitude of the discontinuity wave and the geometry of the bottom, is discussed in detail and some contrasting observations are made.

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变底浅水方程的李对称性与精确解

摘要本文得到了底形变的非线性浅水方程的李对称性，包括水平面、斜面和抛物面底。利用系统在这些对称下的不变性，利用李氏方法得到了控制系统的精确特解。详细讨论了C1 $${C^1}$$不连续波在振幅和底部几何形状的影响下的演化行为，并进行了对比观测。

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.