Interacting helical traveling waves for the Gross–Pitaevskii equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-19 DOI:10.4171/aihpc/32

J. D'avila, M. Pino, María Medina, Rémy Rodiac

引用次数: 2

Abstract

Abstract. We consider the 3D Gross-Pitaevskii equation i∂tψ +∆ψ + (1 − |ψ| )ψ = 0 for ψ : R× R → C and construct traveling waves solutions to this equation. These are solutions of the form ψ(t, x) = u(x1, x2, x3 −Ct) with a velocity C of order ε| log ε| for a small parameter ε > 0. We build two different types of solutions. For the first type, the functions u have a zero-set (vortex set) close to an union of n helices for n ≥ 2 and near these helices u has degree 1. For the second type, the functions u have a vortex filament of degree −1 near the vertical axis e3 and n ≥ 4 vortex filaments of degree +1 near helices whose axis is e3. In both cases the helices are at a distance of order 1/(ε √

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Gross-Pitaevskii方程的相互作用螺旋行波

摘要我们考虑三维Gross-Pitaevskii方程i∂tψ +∆ψ +(1−|ψ|)ψ = 0，对于ψ: rx R→C，构造该方程的行波解。这些解的形式是ψ(t, x) = u(x1, x2, x3−Ct)，对于一个小参数ε > 0，速度C阶为ε| log ε|。我们构建了两种不同类型的解决方案。对于第一类，当n≥2时，函数u有一个接近于n个螺旋并的零集(涡集)，并且在这些螺旋附近u的阶为1。对于第二类，函数u在垂直轴e3附近有一个−1度的涡丝，在轴为e3的螺旋附近有n≥4个+1度的涡丝。在这两种情况下螺旋的距离都是1/(ε√)阶

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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.