Long-time approximations of small-amplitude, long-wavelength FPUT solutions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2023131

Trevor Norton, C. Eugene Wayne

引用次数: 0

Abstract

It is well known that the Korteweg-de Vries (KdV) equation and its generalizations serve as modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation estimates and other such results have been proved in this case. However, situations in which the defocusing modified KdV (mKdV) equation is expected to be the modulation equation have been much less studied. As seen in numerical experiments, the kink solution of the mKdV seems essential in understanding the $\beta$-FPUT recurrence. In this paper, we derive explicit approximation results for solutions of the FPUT using the mKdV as a modulation equation. In contrast to previous work, our estimates allow for solutions to be non-localized as to allow approximate kink solutions. These results allow us to conclude meta-stability results of kink-like solutions of the FPUT.

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长时间近似的小振幅，长波长FPUT解决方案

众所周知，Korteweg-de Vries (KdV)方程及其推广是一般Fermi-Pasta-Ulam-Tsingou (FPUT)格行波解的调制方程。在这种情况下，已经证明了显式近似估计和其他类似的结果。然而，将离焦修正KdV (mKdV)方程作为调制方程的研究却很少。正如在数值实验中所看到的，mKdV的扭结解对于理解$\beta$-FPUT递归似乎是必不可少的。本文利用mKdV作为调制方程，导出了FPUT解的显式逼近结果。与以前的工作相反，我们的估计允许解是非局部的，以允许近似的扭结解。这些结果使我们可以得出FPUT类扭结解的亚稳定性结果。

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.