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孤立子理论中的哈密顿方法

孤立子理论中的哈密顿方法

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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

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 592页

正文语种: 英语

分类: 自然科学

3 张插图图片

31人买过

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

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