Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

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• 作者：Kazuki Aoki ; Nakao Hayashi ; Pavel I. Naumkin
• 关键词：Fourth ; order nonlinear Schrödinger equation ; Global existence ; Non gauge invariant
• 刊名：NoDEA : Nonlinear Differential Equations and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：23
• 期：6
• 全文大小：575 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9004
• 卷排序：23

文摘

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation where \(n=1,2\). We prove global existence of small solutions under the growth condition of \(f\left( u\right) \) satisfying \(\left| \partial _{u}^{j}f\left( u\right) \right| \le C\left| u\right| ^{p-j},\) where \(p>1+\frac{4}{n},0\le j\le 3\).KeywordsFourth-order nonlinear Schrödinger equationGlobal existenceNon gauge invariantMathematics Subject Classification35Q5535Q3535Q51References1.Ben-Artzi, M., Koch, H., Saut, J.C.: Disperion estimates for fourth order Schrödinger equations. C.R.A.S. Série 1 330, 87–92 (2000)2.Dysthe, K.B.: Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. Ser. A 369, 105–114 (1979)CrossRefMATHGoogle Scholar3.Fedoryuk, M.V.: Asymptotic methods in analysis. In: Analysis. I. Integral representations and asymptotic methods. Encyclopaedia of Mathematical Sciences, vol. 13, pp. vi+238. 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Soc. 85(3), 371–379 (2012)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsKazuki Aoki1Nakao Hayashi1Email authorPavel I. Naumkin21.Department of MathematicsGraduate School of Science, Osaka UniversityToyonakaJapan2.Centro de Ciencias Matemáticas, UNAM Campus MoreliaMoreliaMexico About this article CrossMark Print ISSN 1021-9722 Online ISSN 1420-9004 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00030-016-0420-z_Global existence of small solution", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00030-016-0420-z_Global existence of small solution", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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