{"title":"The higher order nonlinear Schrödinger equation with quadratic nonlinearity on the real axis","authors":"A. Faminskii","doi":"10.57262/ade028-0506-413","DOIUrl":null,"url":null,"abstract":"The initial value problem is considered for a higher order nonlinear Schr\\\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional damping large-time decay of solutions without any smallness assumptions is also established. The main difficulty of the study is the non-smooth character of the nonlinearity.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/ade028-0506-413","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
The initial value problem is considered for a higher order nonlinear Schr\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional damping large-time decay of solutions without any smallness assumptions is also established. The main difficulty of the study is the non-smooth character of the nonlinearity.
期刊介绍：
Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.
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