出版社:高等教育出版社
年代:2009
定价:89.0
本书列入《非线性物理科学》,和Springer合作出版。
PartⅠPartialDifferentialEquations
1BasicConcepts
1.1Introduction
1.2Definitions
1.2.1DefinitionofaPDE
1.2.2OrderofaPDE
1.2.3LinearandNonlinearPDEs
1.2.4SomeLinearPartialDifferentialEquations
1.2.5SomeNonlinearPartialDifferentialEquations
1.2.6HomogeneousandInhomogeneousPDEs
1.2.7SolutionofaPDE
1.2.8BoundaryConditions
1.2.9InitialConditions
1.2.10Well-posedPDEs
1.3ClassificationsofaSecond-orderPDE
References
2First-orderPartialDifferentialEquations
2.1Introduction
2.2AdomianDecompositionMethod
2.3TheNoiseTermsPhenomenon
2.4TheModifiedDecompositionMethod
2.5TheVariationalIterationMethod
2.6MethodofCharacteristics
2.7SystemsofLinearPDEsbyAdomianMethod
2.8SystemsofLinearPDEsbyVariationalIterationMethod
References
3OneDimensionalHeatFlow
3.1Introduction
3.2TheAdomianDecompositionMethod
3.2.1HomogeneousHeatEquations
3.2.2lnhomogeneousHeatEquations
3.3TheVariationalIterationMethod
3.3.1HomogeneousHeatEquations
3.3.2InhomogeneousHeatEquations
3.4MethodofSeparationofVariables
3.4.1AnalysisoftheMethod
3.4.2InlaomogeneousBoundaryConditions
3.4.3EquationswithLateralHeatLoss
References
4HigherDimensionalHeatFlow
4.1Introduction
4.2AdomianDecompositionMethod
4.2.1TwoDimensionalHeatFlow
4.2.2ThreeDimensionalHeatFlow
4.3MethodofSeparationofVariables
4.3.1TwoDimensionalHeatFlow
4.3.2ThreeDimensionalHeatFlow
References
5OneDimensionalWaveEquation
5.1Introduction
5.2AdomianDecompositionMethod
5.2.1HomogeneousWaveEquations
5.2.2InhomogeneousWaveEquations
5.2.3WaveEquationinanInfiniteDomain
5.3TheVariationalIterationMethod
5.3.1HomogeneousWaveEquations
5.3.2InhomogeneousWaveEquations
5.3.3WaveEquationinanInfiniteDomain
5.4MethodofSeparationofVariables
5.4.1AnalysisoftheMethod
5.4.2InhomogeneousBoundaryConditions
5.5WaveEquationinanInfiniteDomain:DAlembertSolution
References
6HigherDimensionalWaveEquation
6.1Introduction
6.2AdomianDecompositionMethod
6.2.1TwoDimensionalWaveEquation
6.2.2ThreeDimensionalWaveEquation
……
7LaplacesEquation
8NonlinearPartialDifferentialEquations
9LinearandNonlinearPhysicalModels
10NumericalApplicationsandPadeApproximants
11SolitonsandCompactons
PartⅡSolitrayWavesTheory
12SolitaryWavesTheory
13TheFamilyoftheKdVEquations
14KdVandmKdVEquationsofHigher-orders
15FamilyofKdV-typeEquations
16Boussinesq,Klein-GordonandLiouvilleEquations
17Burgers,FisherandRelatedEquations
18FamiliesofCamassa-HolmandSchrodingerEquations
Appendix
AIndefiniteIntegrals
BSeries
CExactSolutionsofBurgersEquation
DPadeApproximantsforWell-KnownFunctions
ETheErrorandGammaFunctions
FInfiniteSeries
Answers
Index
PartialDifferentialEquationsandSolitaryWavesTheoryisdesignedtoserveasatextandareference.Thebookisdesignedtobeaccessibletoadwnncedundergraduateandbeginninggraduatestudentsaswellasresearchmonographtoresearchersinappliedmathematics,scienceandengineering.Thistextisdifferentfromothertextsinthatitexplainsclassicalmethodsinanonabstractwayanditintroducesandexplainshowthenewlydevelopedmethodsprovidemoreconcisemethodstoprovideefficientresults.
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