非阿贝尔欧拉顶

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-02-01 DOI:10.1070/RM9988

Vladimir V. Sokolov

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引用次数: 0

摘要

在[1]，[2]中，提出了构造具有多项式右手边的给定可积系统的可积非交换推广的一般方法。我们将它应用于寻找欧拉顶的非交换类似物。考虑常微分方程组u′=z1-vw，v′=z2-uw，w′=z3-uv，zi∈C，zi̸=0，（1）其中′表示关于t的导数。系统（1）具有第一积分I1=z3u−z1w和I2=z3v−x2w。对于任何i和j，系统uτ=z1 vwI 1I j2，vτ=z2 uwI i 1I k2，wτ=z3 uvI i 1I j2（2）

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Non-Abelian Euler top

In [1], [2] a general approach to constructing integrable non-commutative generalizations of a given integrable system with polynomial right-hand side was proposed. We apply it to finding non-commutative analogues of the Euler top. Consider the system of ODEs u′ = z1 vw, v′ = z2 uw, w′ = z3 uv, zi ∈ C, zi ̸= 0, (1) where ′ means the derivative with respect to t. The system (1) possesses the first integrals I1 = z3u − z1w and I2 = z3v − x2w. For any i and j, the system uτ = z1 vwI 1I j 2 , vτ = z2 uwI i 1I j 2 , wτ = z3 uvI i 1I j 2 (2)

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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.