具有周期势能的格罗斯-皮塔耶夫斯基方程三维解

IF 0.7 4区 数学 Q2 MATHEMATICS
Yu. Karpeshina, Seonguk Kim, R. Shterenberg
{"title":"具有周期势能的格罗斯-皮塔耶夫斯基方程三维解","authors":"Yu. Karpeshina, Seonguk Kim, R. Shterenberg","doi":"10.1090/spmj/1798","DOIUrl":null,"url":null,"abstract":"<p>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 <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G subset-of double-struck upper R cubed\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">\\mathcal {G}\\subset \\mathbb {R}^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that for every <inline-formula content-type=\"math/tex\"> <tex-math> \\vv k\\in \\mathcal {G}</tex-math></inline-formula> there is a solution asymptotically close to a plane wave <inline-formula content-type=\"math/tex\"> <tex-math> Ae^{i\\langle \\vv {k},\\vv {x}\\rangle }</tex-math></inline-formula> as <inline-formula content-type=\"math/tex\"> <tex-math> |\\vv k|\\to \\infty </tex-math></inline-formula>, given <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is sufficiently small.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solutions of Gross–Pitaevskii equation with periodic potential in dimension three\",\"authors\":\"Yu. Karpeshina, Seonguk Kim, R. Shterenberg\",\"doi\":\"10.1090/spmj/1798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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 <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"script upper G subset-of double-struck upper R cubed\\\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\\\"script\\\">G</mml:mi> </mml:mrow> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\\\"double-struck\\\">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathcal {G}\\\\subset \\\\mathbb {R}^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that for every <inline-formula content-type=\\\"math/tex\\\"> <tex-math> \\\\vv k\\\\in \\\\mathcal {G}</tex-math></inline-formula> there is a solution asymptotically close to a plane wave <inline-formula content-type=\\\"math/tex\\\"> <tex-math> Ae^{i\\\\langle \\\\vv {k},\\\\vv {x}\\\\rangle }</tex-math></inline-formula> as <inline-formula content-type=\\\"math/tex\\\"> <tex-math> |\\\\vv k|\\\\to \\\\infty </tex-math></inline-formula>, given <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper A\\\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is sufficiently small.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1798\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1798","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solutions of Gross–Pitaevskii equation with periodic potential in dimension three

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.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.00
自引率
12.50%
发文量
52
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信