{"title":"四阶非线性Schrüdinger方程的散射算子","authors":"N. Hayashi, Yuichiro Kawahara, P. Naumkin","doi":"10.14492/hokmj/2018-907","DOIUrl":null,"url":null,"abstract":"We study the fourth order nonlinear Schrodinger equation \\begin{equation*} i{\\partial }_{t}u-\\frac{1}{4}\\partial _{x}^{4}u=f(u) ,\\quad (t,x)\\in \\mathbb{R}\\times \\mathbb{R}, \\end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Scattering operator for the fourth order nonlinear Schrüdinger equation\",\"authors\":\"N. Hayashi, Yuichiro Kawahara, P. Naumkin\",\"doi\":\"10.14492/hokmj/2018-907\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the fourth order nonlinear Schrodinger equation \\\\begin{equation*} i{\\\\partial }_{t}u-\\\\frac{1}{4}\\\\partial _{x}^{4}u=f(u) ,\\\\quad (t,x)\\\\in \\\\mathbb{R}\\\\times \\\\mathbb{R}, \\\\end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.\",\"PeriodicalId\":55051,\"journal\":{\"name\":\"Hokkaido Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hokkaido Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14492/hokmj/2018-907\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hokkaido Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14492/hokmj/2018-907","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Scattering operator for the fourth order nonlinear Schrüdinger equation
We study the fourth order nonlinear Schrodinger equation \begin{equation*} i{\partial }_{t}u-\frac{1}{4}\partial _{x}^{4}u=f(u) ,\quad (t,x)\in \mathbb{R}\times \mathbb{R}, \end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.
期刊介绍：
The main purpose of Hokkaido Mathematical Journal is to promote research activities in pure and applied mathematics by publishing original research papers. Selection for publication is on the basis of reports from specialist referees commissioned by the editors.
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