偏微分方程与孤波理论

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.