{"title":"On recovering the nonlinearity for generalized higher-order Schrödinger equations","authors":"Zachary Lee, Xueying Yu","doi":"10.3934/ipi.2023039","DOIUrl":null,"url":null,"abstract":"In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\\\"odinger equations to higher-order Schr\\\"odinger equations with a more general nonlinearity. More precisely, we consider a spatially-localized nonlinear higher-order Schr\\\"odinger equation and recover the spatially-localized coefficient by the solutions with data given by small-amplitude wave packets.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems and Imaging","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ipi.2023039","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a spatially-localized nonlinear higher-order Schr\"odinger equation and recover the spatially-localized coefficient by the solutions with data given by small-amplitude wave packets.
期刊介绍：
Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing.
This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.
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