非线性物理科学：偏微分方程与孤波理论

图书标准信息

• 作者 [美]佤斯瓦茨 著
• 出版社 高等教育出版社
• 出版时间 2009-05
• 版次 1
• ISBN 9787040254808
• 定价 96.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 737页
• 字数 820千字
• 正文语种 英语
• 丛书 非线性物理科学

【内容简介】

PartialDifferentialEquationsandSolitaryWavesTheoryisaself-containedbookdividedintotwoparts：PartIisacoherentsurveybringingtogethernewlydevelopedmethodsforsolvingPDEs.Whilesometraditionaltechniquesarepre-sented,thispartdoesnotrequirethoroughunderstandingofabstracttheoriesorcompactconcepts.Well-selectedworkedexamplesandexercisesshallguidethereaderthroughthetext.PartIIprovidesanextensiveexpositionofthesolitarywavestheory.ThisparthandlesnonlinearevolutionequationsbymethodssuchasHirotasbilinearmethodorthetanh-cothmethod.Aself-containedtreatmentispresentedtodiscusscompleteintegrabilityofawideclassofnonlinearequa-tions.Thispartpresentsinanaccessiblemannerasystematicpresentationofsolitons,multi-solitonsolutions,kinks,peakons,cuspons,andcompactons.

Whilethewholebookcanbeusedasatextforadvancedundergraduateandgraduatestudentsinappliedmathematics,physicsandengineering,PartIIwillbemostusefulforgraduatestudentsandresearchersinmathematics,engineer-ing,andotherrelatedfields.

【目录】

PartIPartialDifferentialEquations

1BasicConcepts

1.1Introduction

1.2Definitions

1.2.1DefinitionofaPDE

1.2.2OrderofaPDE

1.2.3LinearandNonlinearPDEs

1.2.4SomeLinearPartialDifferentialEquations

1.2.5SomeNonlinearPartialDifferentialEquations..

1.2.6HomogeneousandInhomogeneot,sPDEs

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

3.2.2InhomogeneousHeatEquations

3.3TheVariationalIterationMethod

3.3.1HomogeneousHeatEquations

3.3.2InhomogeneousHeatEquations

3.4MethodofSeparationofVariables

3.4.1AnalysisoftheMethod

3.4.2InhomogeneousBoundaryConditions

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

6.3MethodofSeparationofVariables

6.3.1TwoDimensionalWaveEquation

6.3.2ThreeDimensionalWaveEquation

References

7LaplacesEquation

7.1Introduction

7.2AdomianDecompositionMethod

7.2.1TwoDimensionalLaplacesEquation...

7.3TheVariationalIterationMethod

7.4MethodofSeparationofVariables

7.4.1LaplacesEquationinTwoDimensions..

7.4.2LaplacesEquationinThreeDimensions

7.5LaplacesEquationinPolarCoordinates

7.5.1LaplacesEquationforaDisc

7.5.2LaplacesEquationforanAnnulus

References

8NonlinearPartialDifferentialEquations

8.1Introduction

8.2AdomianDecompositionMethod

8.2.1CalculationofAdomianPolynomials...

8.2.2AlternativeAlgorithmforCalculatingAdomianPolynomials

8.3NonlinearODEsbyAdomianMethod

8.4NonlinearODEsbyVIM

8.5NonlinearPDEsbyAdomianMethod

8.6NonlinearPDEsbyVIM

8.7NonlinearPDEsSystemsbyAdomianMethod..

8.8SystemsofNonlinearPDEsbyVIM

References

9LinearandNonlinearPhysicalModels

9.1Introduction

9.2TheNonlinearAdvectionProblem

9.3TheGoursatProblem

9.4TheKlein-GordonEquation

9.4.1LinearKlein-GordonEquation

9.4.2NonlinearKlein-GordonEquation

9.4.3TheSine-GordonEquation

9.5TheBurgersEquation

9.6TheTelegraphEquation

9.7SchrodingerEquation

9.7.1TheLinearSchrodingerEquation

9.7.2TheNonlinearSchrodingerEquation

9.8Korteweg-deVriesEquation

9.9Fourth-orderParabolicEquation

9.9.1EquationswithConstantCoefficients

9.9.2EquationswithVariableCoefficients

References

10NumericalApplicationsandPadeApproximants

10.1Introduction

10.2OrdinaryDifferentialEquations

10.2.1PerturbationProblems

10.2.2NonperturbedProblems

10.3PartialDifferentialEquations

10.4ThePadeApproximants

10.5Pad6ApproximantsandBoundaryValueProblems

References

11SolitonsandCompaetons

11.1Introduction

11.2Solitons

11.2.1TheKdVEquation

11.2.2TheModifiedKdVEquation

11.2.3TheGeneralizedKdVEquation

11.2.4TheSine-GordonEquation

11.2.5TheBoussinesqEquation

11.2.6TheKadomtsev-PetviashviliEquation

11.3Compactons

11.4TheDefocusingBranchofK(n,n)

References

PartHSolitrayWavesTheory

12SolitaryWavesTheory

12.1Introduction

12.2Definitions

12.2.1DispersionandDissipation

12.2.2TypesofTravellingWaveSolutions

12.2.3NonanalyticSolitaryWaveSolutions

12.3AnalysisoftheMethods

12.3.1TheTanh-cothMethod

12.3.2TheSine-cosineMethod

12.3.3HirotasBilinearMethod

12.4ConservationLaws

References