孤立子理论中的哈密顿方法

图书标准信息

• 作者 L.D.法捷耶夫（Ludwig D.Faddeev） 著
• 出版社 世界图书出版公司
• 出版时间 2013-03
• 版次 1
• ISBN 9787510058264
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 592页
• 正文语种 英语

【内容简介】

　　ThebookisbasedontheHamiltonianinterpretationofthemethod，hencethetitle.MethodsofdifferentialgeometryandHamiitonianformalisminparticularareverypopularinmodernmathematicalphysics.ItispreciselythegeneralHamiltonianformalismthatpresentstheinversescatteringmethodinitsmostelegantform.Moreover，theHamiltonianformalismprovidesalinkbetweenclassicalandquantummechanics.Sothebookisnotonlyanintroductiontotheclassicalsolitontheorybutalsothegroundworkforthequantumtheoryofsolitons，tobediscussedinanothervolume.
　　Thebookisaddressedtospecialistsinmathematicalphysics.Thishasdeterminedthechoiceofmaterialandthelevelofmathematicalrigour.Wehopethatitwillalsobeofinteresttomathematiciansofotherspecialitiesandtotheoreticalphysicistsaswell.Still，beingamathematicaltreatiseitdoesnotcontainapplicationsofsolitontheorytospecificphysicalphenomena.

【目录】

IntroductionReferences
PartOneTheNonlinearSchrodingerEquation(NSModel)
ChapterⅠZeroCurvatureRepresentation
1.FormulationoftheNSModel
2.ZeroCurvatureCondition
3.PropertiesoftheMonodromyMatrixintheQuasi-PeriodicCase
4.LocalIntegralsoftheMotion
5.TheMonodromyMatrixintheRapidlyDecreasingCase
6.AnalyticPropertiesofTransitionCoefficients
7.TheDynamicsofTransitionCoefficients
8.TheCaseofFiniteDensity.JostSolutions
9.TheCaseofFiniteDensity.TransitionCoefficients
10.TheCaseofFiniteDensity.TimeDynamicsandIntegralsoftheMotion
1.NotesandReferences
References
ChapterⅡTheRiemannProblem
1.TheRapidlyDecreasingCase.FormulationoftheRiemannProblem
2.TheRapidlyDecreasingCase.AnalysisoftheRiemannProblem
3.ApplicationoftheInverseScatteringProblemtotheNSModel
4.RelationshipBetweentheRiemannProblemMethodandtheGelfand-Levitan-MarchenkoIntegralEquationsFormulation
5.TheRapidlyDecreasingCase.SolitonSolutions
6.SolutionoftheInverseProblemintheCaseofFiniteDensity.TheRiemannProblemMethod
7.SolutionoftheInverseProblemintheCaseofFiniteDensity.TheGelfand-Levitan-MarchenkoFormulation
8.SolitonSolutionsintheCaseofFiniteDensity
9.NotesandReferencesReferences
ChapterⅢTheHamiltonianFormulation
1.FundamentalPoissonBracketsandthe/"-Matrix
2.PoissonCommutativityoftheMotionIntegralsintheQuasi-PeriodicCase
3.DerivationoftheZeroCurvatureRepresentationfromtheFundamentalPoissonBrackets
4.IntegralsoftheMotionintheRapidlyDecreasingCaseandintheCaseofFiniteDensity
5.TheA-OperatorandaHierarchyofPoissonStructures
6.PoissonBracketsofTransitionCoefficientsintheRapidlyDecreasingCase
7.Action-AngleVariablesintheRapidlyDecreasingCase
8.SolitonDynamicsfromtheHamiltonianPointofView
9.CompleteIntegrabilityintheCaseofFiniteDensity
10.NotesandReferences
References

PartTwoGeneralTheoryofIntegrableEvolutionEquations
ChapterⅠBasicExamplesandTheirGeneralProperties
1.FormulationoftheBasicContinuousModels
2.ExamplesofLatticeModels
3.ZeroCurvatureRepresentation'saMethodforConstructingIntegrableEquations
4.GaugeEquivalenceoftheNSModel(#=-1)andtheHMModel
5.HamiltonianFormulationoftheChiralFieldEquationsandRelatedModels
6.TheRiemannProblemasaMethodforConstructingSolutionsofIntegrableEquations
7.ASchemeforConstructingtheGeneralSolutionoftheZeroCurvatureEquation.ConcludingRemarksonIntegrableEquations
8.NotesandReferences
References
ChapterⅡFundamentalContinuousModels
1.TheAuxiliaryLinearProblemfortheHMModel
2.TheInverseProblemfortheHMModel
3.HamiltonianFormulationoftheHMModel4.TheAuxiliaryLinearProblemfortheSGModel
5.TheInverseProblemfortheSGModel
6.HamiltonianFormulationoftheSGModel
ChapterⅢFundamentalModelsontheLattice
ChapterⅣLie-AlgebraicApproachtotheClassificationandAnalysisofIntegrableModelsConclusionListofSymbolsIndex
……
Conclusion
ListofSymbols
Index