经典可积系统导论

图书标准信息

• 作者 [法]贝博龙（Babelon O.） 著
• 出版社 世界图书出版公司
• 出版时间 2009-05
• 版次 1
• ISBN 9787510004575
• 定价 88.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 602页

【内容简介】

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.

【目录】

1Introduction
2Integrabledynamicalsystems
2.1Introduction
2.2TheLiouvilletheorem
2.3Action-anglevariables
2.4Laxpairs
2.5Existenceofanr-matrix
2.6Commutingflows
2.7TheKeplerproblem
2.8TheEulertop
2.9TheLagrangetop
2.10TheKowalevskitop
2.11TheNeumannmodel
2.12Geodesicsonanellipsoid
2.13SeparationofvariablesintheNeumannmodel
3Synopsisofintegrablesystems
3.1ExamplesofLaxpairswithspectralparameter
3.2TheZakharov-Shabatconstruction
3.3CoadjointorbitsandHamiltonianformalism
3.4Elementaryflowsandwavefunction
3.5Factorizationproblem
3.6Tau.functions
3.7Integrablefieldtheoriesandmonodromymatrix
3.8Abelianization
3.9Poissonbracketsofthemonodromymatrix
3.10Thegroupofdressingtransformations
3.11Solitonsolutions
4Algebraicmethods
4.1TheclassicalandmodifiedⅥln9-Baxterequations
4.2AlgebraicmeaningoftheclassicalYan9-Baxterequations
4.3Adler-Kostant-Symesscheme
4.4Constructionofintegrablesystems
4.5Solvingbyfactorization
4.6TheopenTodachain
4.7Ther.matrixoftheTodamodels
4.8SolutionoftheopenTodachain
4.9TodasystemandHamiltonianreduction
4.10TheLaxpairoftheKowalevskitop
5Analyticalmethods
5.1Thespectralcurve
5.2Theeigenvectorbundle
5.3Theadjointlinearsystem
5.4Timeevolution
5.5Theta-functionsformulae
5.6Baker-Akhiezerfunctions
5.7Linearizationandthefactorizationproblem
5.8Tau-functions
5.9Symplecticform
5.10Separationofvariablesandthespectralcurve
5.11Action-anglevariables
5.12Riemannsurfacesandintegrability
5.13TheKowalevskitop
5.14Infinite-dimensionalsystems
6TheclosedT0dachain
6.1Themodel
6.2Thespectralcurve
6.3Theeigenvectors
6.4Reconstructionformula
6.5Symplecticstructure
6.6TheSklyaninapproach
6.7ThePoissonbrackets
6.8Realityconditions
7TheCalogero-Mosermodel
7.1ThespinCaloger0-Mosermodel
……
8Isomonodromicdeformations
9Grassmannianandintegrablehierarchies
10TheKPhierarchy
11TheKdVhierarchy
12TheTodafieldtheories
13Classicalinversescatteringmethod
14Symplecticgeometry
15Riemannsurfaces
16Liealgebras
Index