Springer.Zhidkov.P.E.Korteweg.de.Vries.and.nonlinear.Schroedinger.equation.[LNM1756.Springer.2001].(152.p)

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1、LectureNotesinMathematics1756Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,Paris3BerlinHeidelbergNewYorkBarcelonaHongKongLondonMilanParisSingaporeTokyoPeterE.ZhidkovKorteweg-deVriesandNonlinearSchrödingerEquations:QualitativeTheory123AuthorPeter

2、E.ZhidkovBogoliubovLaboratoryofTheoreticalPhysicsJointInstituteforNuclearResearch141980Dubna,RussiaE-mail:zhidkov@thsun1.jinr.ruCataloging-in-PublicationDataappliedforMathematicsSubjectClassification(2000):34B16,34B40,35D05,35J65,35Q53,35Q55,35P30,37A05

3、,37K45ISSN0075-8434ISBN3-540-41833-4Springer-VerlagBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broa

4、dcasting,reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpr

5、inger-Verlag.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.Springer-VerlagBerlinHeidelbergNewYorkamemberofBertelsmannSpringerScience+BusinessMediaGmbHhttp://www.springer.de©Springer-VerlagBerlinHeidelberg2001PrintedinGermanyTypesetting:Cam

6、era-readyTEXoutputbytheauthorsSPIN:1075993641/3142-543210-Printedonacid-freepaperContentsPageIntroductionINotation5Chapter1.Evolutionaryequations.Resultsonexistence91.1The(generalized)Korteweg-deVriesequation(KdVE)101.2ThenonlinearSchr6dingerequation(NL

7、SE)261.3Ontheblowingupofsolutions361.4Additionalremarks.37Chapter2.Stationaryproblems392.1Existenceofsolutions.AnODEapproach422.2Existenceofsolutions.Avariationalmethod492.3Theconcentration-compactnessmethodofP.L.Lions562.4Onbasispropertiesofsystemsofso

8、lutions622.5Additionalremarks76Chapter3.Stabilityofsolutions793.1Stabilityofsoliton-likesolutions803.2StabilityofkinksfortheKdVE903.3StabilityofsolutionsoftheNLSEnonvanishingasjxjoo943.4Additionalremarks103Chapter4.Invariantmeasu