边值问题中具有简单焦散的有效半经典渐近性

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI:10.1134/S1061920825600072

S.Yu. Dobrokhotov, V.E. Nazaikinskiih, A.V. Tsvetkova, A.V. Turin

{"title":"边值问题中具有简单焦散的有效半经典渐近性","authors":"S.Yu. Dobrokhotov, V.E. Nazaikinskiih, A.V. Tsvetkova, A.V. Turin","doi":"10.1134/S1061920825600072","DOIUrl":null,"url":null,"abstract":" In this paper we continue to develop the approach to constructing global uniform asymptotics of solutions of (pseudo)differential problems in terms of special functions based on the theory of the Maslov canonical operator. In particular, we show that if the corresponding Lagrangian manifold has a fold-type singularity, then the canonical operator on it is represented via the Airy function Ai and its derivative of complex arguments. This approach is illustrated by a known problem about construction of asymptotic eigenfunctions of the Laplace operator in an elliptic domain with Dirichlet boundary conditions. DOI 10.1134/S1061920825600072 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"28 - 43"},"PeriodicalIF":1.7000,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Efficient Semiclassical Asymptotics with Simple Caustics in a Boundary Value Problem\",\"authors\":\"S.Yu. Dobrokhotov, V.E. Nazaikinskiih, A.V. Tsvetkova, A.V. Turin\",\"doi\":\"10.1134/S1061920825600072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" In this paper we continue to develop the approach to constructing global uniform asymptotics of solutions of (pseudo)differential problems in terms of special functions based on the theory of the Maslov canonical operator. In particular, we show that if the corresponding Lagrangian manifold has a fold-type singularity, then the canonical operator on it is represented via the Airy function Ai and its derivative of complex arguments. This approach is illustrated by a known problem about construction of asymptotic eigenfunctions of the Laplace operator in an elliptic domain with Dirichlet boundary conditions. DOI 10.1134/S1061920825600072 \",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"32 1\",\"pages\":\"28 - 43\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920825600072\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920825600072","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们基于马斯洛夫正则算子理论，继续发展了用特殊函数构造（伪）微分问题解的全局一致渐近的方法。特别地，我们证明了如果相应的拉格朗日流形具有折叠型奇点，则其上的正则算子可以通过Airy函数Ai及其复参数的导数来表示。用一个已知的具有狄利克雷边界条件的椭圆域上拉普拉斯算子的渐近特征函数的构造问题说明了这种方法。DOI 10.1134 / S1061920825600072

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Efficient Semiclassical Asymptotics with Simple Caustics in a Boundary Value Problem

In this paper we continue to develop the approach to constructing global uniform asymptotics of solutions of (pseudo)differential problems in terms of special functions based on the theory of the Maslov canonical operator. In particular, we show that if the corresponding Lagrangian manifold has a fold-type singularity, then the canonical operator on it is represented via the Airy function Ai and its derivative of complex arguments. This approach is illustrated by a known problem about construction of asymptotic eigenfunctions of the Laplace operator in an elliptic domain with Dirichlet boundary conditions.

DOI 10.1134/S1061920825600072

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

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.