lie algebras geometry and toda-type systems[Razumov]

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1、ThisbookintroducestheuseofLiealgebraanddifferentialge-ometrymethodstostudynonlinearintegrablesystemsofTodatype.Manychallengingproblemsintheoreticalphysicsarerelatedtothesolutionofnonlinearsystemsofpartialdifferentialequa-tions.Oneofthemostfruitfulapproachesinrecentyearshasresultedfromam

2、ergingofgroupalgebraicandgeometrictech-niques.Thebookprovidesacomprehensiveintroductiontothisexcitingbranchofscience.Chapters1and2reviewthebasicno-tionsofLiealgebrasanddifferentialgeometry,withanemphasisonfurtherapplicationstointegrablenonlinearsystems.Chapter3containsaderivationofToda-

3、typesystemsandtheirgeneralsolu-tionsbasedonLiealgebraanddifferentialgeometrymethods.Thefinalchapterexaminestheexplicitsolutionsofthecorrespondingequations.Thebookiswritteninanaccessiblelecturenotestyle,withmanyexamplesandexercisesgiventoillustratekeypointsandtoreinforceunderstanding.Thi

4、sbookwillbeofinteresttograduatestudentsandre-searchersintheoreticalphysicicsandappliedmathematics.CAMBRIDGELECTURENOTESINPHYSICS8GeneralEditors:P.Goddard,J.YeomansLieAlgebras,Geometry,andToda-typeSystemsCAMBRIDGELECTURENOTESINPHYSICS1.Clarke:TheAnalysisofSpace-TimeSingularities2.Dorey:E

5、xactS-MatricesinTwoDimensionalQuantumFieldTheory3.Sciama:ModernCosmologyandtheDarkMatterProblem4.Veltman:Diagrammatica-ThePathtoFeynmanRules5.Cardy:ScalingandRenormalizationinStatisticalPhysics6.Heusler:BlackHoleUniquenessTheorems7.ColesandEllis:IstheUniverseOpenorClosed?8.RazumovandSav

6、eliev:LieAlgebras,Geometry,andToda-typeSystemsLieAlgebras,Geometry,andToda-typeSystemsA.V.RAZUMOVM.V.SAVELIEVInstituteforHighEnergyPhysics,Protvino,RussiaCAMBRIDGEUNIVERSITYPRESSPUBLISHEDBYTHEPRESSSYNDICATEOFTHEUNIVERSITYOFCAMBRIDGEThePittBuilding,TrumpingtonStreet,CambridgeCB21RPUnited

7、KingdomCAMBRIDGEUNIVERSITYPRESSTheEdinburghBuilding,CambridgeCB22RU,UnitedKingdom40West20thStreet,NewYork,NY10011-4211,USA10StamfordRoad,Oakleigh,Melbourne3166,Australia?CambridgeUniversityPress1997Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcol