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1、ClassicalandQuantumNonlinearIntegrableSystemsTheoryandApplicationsEditedbyAKunduSahaInstituteofNuclearPhysicsCalcutta,IndiaInstituteofPhysicsPublishingBristolandPhiladelphiaCopyright©2003IOPPublishingLtd.cIOPPublishingLtd2003Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrieva
2、lsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutthepriorpermissionofthepublisher.MultiplecopyingispermittedinaccordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgencyunderthetermsofitsagreementwithUniversitiesUK(UUK).BritishLibraryCa
3、taloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.ISBN0750309598LibraryofCongressCataloging-in-PublicationDataareavailableCommissioningEditor:TomSpicerProductionEditor:SimonLaurensonProductionControl:SarahPlentyCoverDesign:VictoriaLeBillonMarketing:NicolaNeweyan
4、dVerityCookePublishedbyInstituteofPhysicsPublishing,whollyownedbyTheInstituteofPhysics,LondonInstituteofPhysicsPublishing,DiracHouse,TempleBack,BristolBS16BE,UKUSOfÞce:InstituteofPhysicsPublishing,ThePublicLedgerBuilding,Suite929,150SouthIndependenceMallWest,Philadelphia,PA19106,USATypesetbySunriseS
5、ettingLtd,Torquay,Devon,UKPrintedintheUKbyMPGBooksLtd,Bodmin,CornwallCopyright©2003IOPPublishingLtd.ContentsPrefacePARTIClassicalSystems1AjourneythroughtheKortewegdeVriesequationMLakshmanan1.1Introduction1.2Nonlineardispersivewaves:ScottRussellphenomenonandsolitarywaves1.2.1KdVequationandcnoidalwave
6、sandthesolitarywaves1.3TheFermiÐPastaÐUlam(FPU)numericalexperimentsonanharmoniclattices1.3.1TheFPUlatticeandrecurrencephenomenon1.4TheKdVequationagain!1.4.1AsymptoticanalysisandtheKdVequation1.5NumericalexperimentsofZabuskyandKruskal:thebirthofsolitons1.5.1Periodicboundaryconditions1.5.2Initialcondi
7、tionwithjusttwosolitarywaves1.6HirotaÕsbilinearizationmethod:explicitsolitonsolutions1.6.1One-solitonsolution1.6.2Two-solitonsolution1.6.3N-solitonsolutions1.6.4Asymptoticanalysis1.7TheMiuratransforma
