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[法] 贝博龙 (Babelon O.) 著 / 世界图书出版公司 / 2009-05 / 平装
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providesathoroughintroductiontothetheoryofclassicalintegrablesystems,discussingthevariousapproachestothesubjectandexplainingtheirinterrelations.Thebookbeginsbyintroducingthecentralideasofthetheoryofintegrablesystems,basedonLaxrepresentations,loopgroupsandRiemannsurfaces.Theseideasarethenillustratedwithdetailedstudiesofmodelsystems.Theconnectionbetweenisomon-odromicdeformationandintegrabilityisdiscussed,andintegrablefieldtheoriesarecoveredindetail.TheKP,KdVand'lbdahierarchiesareexplainedusingthenotionofGrassmannian,vertexoperatorsandpseudo-differentialoperators.Achapterisdevotedtotheinversescatteringmethodandthreecomplementarychapterscoverthenecessarymathematicaltoolsfromsymplecticgeometry,RiemannsurfacesandLiealgebras.Thebookcontainsmanyworkedexamplesandissuitableforuseasatextbookongraduatecourses.Italsoprovidesacomprehensivereferenceforresearchersalreadyworkinginthefield.OLIVIERBABELONhasbeenamemberoftheCentreNationaldelaRechercheSci-entifique(CNRS)since1978.HeworksattheLaboratoiredePhysiqueTheoriqueetHautesEnergies(LPTRE)attheUniversityofParisVI-ParisVII.Hismainfieldsofinterestareparticlephysics,gaugetheoriesandintegrablessystems.MICHELTALONhasbeenamemberoftheCNRSsince1977.HeworksattheLPTHEattheUniversityofParisVI-ParisVII.Heisinvolvedinthecomputationofradiativecorrectionsandanomaliesingaugetheoriesandintegrablesystems.DENISBERNARDhasbeenamemberoftheCNRSsince1988.HecurrentlyworksattheServicedePhysiqueTheoriquedeSaclay.Hismainfieldsofinterestareconforma[fieldtheoriesandintegrablesystems,andotheraspectsofstatisticalfieldtheories,includingstatisticalturbulence.
1Introduction2Integrabledynamicalsystems2.1Introduction2.2TheLiouvilletheorem2.3Action-anglevariables2.4Laxpairs2.5Existenceofanr-matrix2.6Commutingflows2.7TheKeplerproblem2.8TheEulertop2.9TheLagrangetop2.10TheKowalevskitop2.11TheNeumannmodel2.12Geodesicsonanellipsoid2.13SeparationofvariablesintheNeumannmodel3Synopsisofintegrablesystems3.1ExamplesofLaxpairswithspectralparameter3.2TheZakharov-Shabatconstruction3.3CoadjointorbitsandHamiltonianformalism3.4Elementaryflowsandwavefunction3.5Factorizationproblem3.6Tau.functions3.7Integrablefieldtheoriesandmonodromymatrix3.8Abelianization3.9Poissonbracketsofthemonodromymatrix3.10Thegroupofdressingtransformations3.11Solitonsolutions4Algebraicmethods4.1TheclassicalandmodifiedⅥln9-Baxterequations4.2AlgebraicmeaningoftheclassicalYan9-Baxterequations4.3Adler-Kostant-Symesscheme4.4Constructionofintegrablesystems4.5Solvingbyfactorization4.6TheopenTodachain4.7Ther.matrixoftheTodamodels4.8SolutionoftheopenTodachain4.9TodasystemandHamiltonianreduction4.10TheLaxpairoftheKowalevskitop5Analyticalmethods5.1Thespectralcurve5.2Theeigenvectorbundle5.3Theadjointlinearsystem5.4Timeevolution5.5Theta-functionsformulae5.6Baker-Akhiezerfunctions5.7Linearizationandthefactorizationproblem5.8Tau-functions5.9Symplecticform5.10Separationofvariablesandthespectralcurve5.11Action-anglevariables5.12Riemannsurfacesandintegrability5.13TheKowalevskitop5.14Infinite-dimensionalsystems6TheclosedT0dachain6.1Themodel6.2Thespectralcurve6.3Theeigenvectors6.4Reconstructionformula6.5Symplecticstructure6.6TheSklyaninapproach6.7ThePoissonbrackets6.8Realityconditions7TheCalogero-Mosermodel7.1ThespinCaloger0-Mosermodel……8Isomonodromicdeformations9Grassmannianandintegrablehierarchies10TheKPhierarchy11TheKdVhierarchy12TheTodafieldtheories13Classicalinversescatteringmethod14Symplecticgeometry15Riemannsurfaces16LiealgebrasIndex
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