Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-29 DOI:10.3934/jgm.2021019

W. Sarlet, T. Mestdag

引用次数: 1

Abstract

The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather unusual approach because velocity-dependent transformations in general do not preserve the second-order character of differential equations. Moreover, at least in the case of linear transformations, such a velocity-dependent one defines by itself a second-order system, which need not have anything to do, in principle, with the given system or its reformulation. This aspect, and the related questions of compatibility it raises, seem to have been overlooked in the existing literature. The purpose of this paper is to clarify this issue and to suggest topics for further research in conjunction with the general theory of decoupling in a differential geometric context.

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解耦线性二阶微分方程相位同步方法的兼容性问题

在一些论文中，所谓的相位同步方法被认为是一种通过坐标和速度的线性变换来解耦线性二阶微分方程组的方法。这是一种相当不寻常的方法，因为与速度相关的变换通常不能保持微分方程的二阶特性。此外，至少在线性变换的情况下，这样一个速度相关的变换本身定义了一个二阶系统，原则上，它不需要与给定的系统或它的重新表述有任何关系。这方面，以及与之相关的兼容性问题，似乎在现有文献中被忽视了。本文的目的是澄清这一问题，并结合微分几何背景下的解耦一般理论提出进一步研究的主题。

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.