{"title":"Local well-posedness of a generalized nonlinear Schrödinger equation with cubic–quintic nonlinearity","authors":"R. Adams","doi":"10.1016/j.ijleo.2021.168118","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>In this article, we study the Cauchy Problem associated to the generalized cubic–quintic Schrödinger equation which has been used for the description of propagation pulses in </span>optical fibers. Using gauge transforms and a derivation process, we prove under some regularity assumptions, the local well-posedness. Additionally, a global </span><span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> bound is established for the solution.</p></div>","PeriodicalId":19513,"journal":{"name":"Optik","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optik","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0030402621016648","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 1
Abstract
In this article, we study the Cauchy Problem associated to the generalized cubic–quintic Schrödinger equation which has been used for the description of propagation pulses in optical fibers. Using gauge transforms and a derivation process, we prove under some regularity assumptions, the local well-posedness. Additionally, a global bound is established for the solution.
期刊介绍：
Optik publishes articles on all subjects related to light and electron optics and offers a survey on the state of research and technical development within the following fields:
Optics:
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Optical and micro-optical components, diffractive optics, devices and systems-
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Information optics, image formation and processing, holographic techniques, microscopes and spectrometer techniques, and image analysis-
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Physiological optics-
As well as other related topics.
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