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1、TheDirectMethodinSolitonTheoryCAMBRIDGETRACTSINMATHEMATICSGeneralEditorsB.BOLLOBAS,W.FULTON,A.KATOK,F.KIRWAN,´P.SARNAK,B.SIMON155TheDirectMethodinSolitonTheoryTheDirectMethodinSolitonTheoryRYOGOHIROTATranslatedfromJapaneseandeditedbyAtsushiNagai,JonNi
2、mmoandClaireGilsoncambridgeuniversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridgecb22ru,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.o
3、rgInformationonthistitle:www.cambridge.org/9780521836609©IwanamiShoten1992Englishtranslation:CambridgeUniversityPress2004Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofa
4、nypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2004isbn-13978-0-511-21663-3eBook(NetLibrary)isbn-100-511-21663-7eBook(NetLibrary)isbn-13978-0-521-83660-9hardbackisbn-100-521-83660-3hardbackCambridgeU
5、niversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.ContentsForewordpageviiPrefaceix
6、1Bilinearizationofsolitonequations11.1Solitarywavesandsolitons11.2Nonlinearityanddispersion21.3Solutionsofnonlineardifferentialequations91.4Linearizationofnonlineardifferentialequations121.5Essentialsofthedirectmethod191.6TheD-operator,anewdifferentia
7、loperator271.7Bilinearizationofnonlineardifferentialequations371.8Solutionsofbilinearequations461.9Transformationfrombilineartononlinearform582Determinantsandpfaffians602.1Introduction602.2Pfaffians612.3Exterioralgebra642.4Expressionsforgeneraldetermina
8、ntsandwronskians662.5LaplaceexpansionsofdeterminantsandPluckerrelations¨702.6Jacobiidentitiesfordeterminants772.7Specialdeterminants842.8Pfaffianidentities922.9Expansionformulaeforthepfaffian(a1,a2,1,2,...,2n)972.10Additionformulaeforpfaffians992