On the Steadiness of Symmetric Solutions to Two Dimensional Dispersive Models

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-15 DOI:10.1007/s00021-024-00869-0

Long Pei, Fengyang Xiao, Pan Zhang

引用次数: 0

Abstract

In this paper, we consider the steadiness of symmetric solutions to two dispersive models in shallow water and hyperelastic mechanics, respectively. These models are derived previously in the two-dimensional setting and can be viewed as the generalization of the Camassa–Holm and Kadomtsev–Petviashvili equations. For these two models, we prove that the symmetry of classical solutions implies steadiness in the horizontal direction. We also confirm the connection between symmetry and steadiness for solutions in weak formulation, which covers in particular the peaked solutions.

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论二维分散模型对称解的稳定性

在本文中，我们分别考虑了浅水和超弹性力学中两个分散模型对称解的稳定性。这些模型是之前在二维环境中推导出来的，可视为卡马萨-霍尔姆方程和卡多姆采夫-佩特维亚什维利方程的广义化。对于这两个模型，我们证明了经典解的对称性意味着水平方向上的稳定性。我们还证实了弱公式解的对称性和稳定性之间的联系，尤其是峰值解。

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.