{"title":"Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side","authors":"","doi":"10.1134/s0040577924010021","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> A model Helmholtz equation with a localized right-hand side is considered. When writing asymptotics of a solution satisfying the limit absorption principle, a Lagrangian surface naturally appears that has a logarithmic singularity at one point. Because of this singularity, the solution is localized not only in a neighborhood of the projection of the Lagrangian surface onto the coordinate space but also in a neighborhood of a certain ray “escaping” from the Lagrangian surface and going into the region forbidden in the classical approximation. </p> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924010021","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
A model Helmholtz equation with a localized right-hand side is considered. When writing asymptotics of a solution satisfying the limit absorption principle, a Lagrangian surface naturally appears that has a logarithmic singularity at one point. Because of this singularity, the solution is localized not only in a neighborhood of the projection of the Lagrangian surface onto the coordinate space but also in a neighborhood of a certain ray “escaping” from the Lagrangian surface and going into the region forbidden in the classical approximation.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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