Solutions of Gross–Pitaevskii equation with periodic potential in dimension three

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1798

Yu. Karpeshina, Seonguk Kim, R. Shterenberg

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引用次数: 0

Abstract

Quasiperiodic solutions of the Gross–Pitaevskii equation with a periodic potential in dimension three are studied. It is proved that there is an extensive “nonresonant” set G ⊂ R 3 \mathcal {G}\subset \mathbb {R}^3 such that for every \vv k\in \mathcal {G} there is a solution asymptotically close to a plane wave Ae^{i\langle \vv {k},\vv {x}\rangle } as |\vv k|\to \infty , given A A is sufficiently small.

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具有周期势能的格罗斯-皮塔耶夫斯基方程三维解

研究了三维中具有周期势的格罗斯-皮塔耶夫斯基方程的准周期解。研究证明，存在一个广泛的 "非共振 "集合 G ⊂ R 3 \mathcal {G}\subset \mathbb {R}^3 ，这样对于 \mathcal {G} 中的每一个 \vv k\ 都有一个近似接近于平面波 Ae^{i\langle \vv {k},\vv {x}\rangle } 的解，因为 |\vv k|\to \infty ，给定 A A 足够小。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.