A general review on the NLS equation with point-concentrated nonlinearity

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2023-01-01 DOI:10.2478/caim-2023-0004

Lorenzo Tentarelli

引用次数: 0

Abstract

Abstract The paper presents a complete (to the best of the author’s knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.

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具有点集中非线性的NLS方程综述

摘要:本文对具有点集中非线性的NLS方程的现有文献进行了全面(据作者所知)的综述。具体来说，主要包括模型的定义、弱和强局部适定性、全局适定性、驻波的分类和稳定性(轨道和渐近)、爆破分析和具有收缩势的标准NLS方程的推导。并提出了一些相关问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.