非线性波，孤立子和混沌：英文版

　　This revised and updated second edition.of a， highly successful book is the only text at this level to embrace a universai approach to three major developments in classical physics; namely nonlinear waves， solitons and chaos. The authors now include new material on biology and laser theory， and go on to discuss important recent developments such as soliton metamorphosis. .A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Examples of these are coherent entities like nonlinear waves and solitons， as well as the incoherent structures associated with chaos. The first part of the book is a self-contained introduction to general topics associated with nonlinear graduate physics， and would be accessible to final-year undergraduates and beginning graduate students. The remainder of the book， for example the treatment of cylindrical solitons， is more advanced and will have a wide appeal to specialists in a number of branches of physics. Each chapter concludes with a set of problems. ..This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general， it will. be of value to final-year undergraduates and beginning graduate students studying fluid dynamics， plasma physics or applied mathematics.

暂缺《非线性波，孤立子和混沌：英文版》作者简介

Forewordtothefirstedition.
Forewordtothesecondedition
1Introduction
1.1OccurrenceofnonlinearwavesandinstabilitiesinNature
1.1.1Nonlinearphenomenainoureverydayexperience
1.1.2Nonlinearphenomenainthelaboratory
1.2Universalwaveequations
1.2.1TheKorteweg-deVriesandKadomtsev-Petviashviliequationsandafirstlookatsolitons
1.2.2ThenonlinearSchr6dingcrequation
1.2.3Nonlinearoptics
1.3Whatisaplasma?
1.4Wavemodesonawatersurface
1.4.1Mathematicaltheory
1.4.2Comments
1.5Linearstabilityanalysisanditslimitations
1.6Nonlinearstructures
1.6.1Coherentstructuresandpatternformation
1.7ContentsofChapters2-11
2Linearwavesandinstabilitiesininfinitemedia
2.1Introduction
2.2Plasmawaves
2.3CMAdiagrams
2.4Instabilities
2.5TheVlasovequation
2.6Weakinstabilities
Exercises
3Convectiveandnon-convectiveinstabilities;groupvelocityinunstablemedia
3.1Introduction
3.2Kinematicsofunstablewavepackets
3.3Movingcoordinatesystems
3.4Higherdimensionalsystems
3.5Summary
Exercise
4Afirstlookatsurfacewavesandinstabilities
4.1Introduction
4.2Simplesurfacewaves
4.3TheRayleigh-Taylorinstability
4.4TheKelvin-Helmholtzinstability
4.5Solid-liquidinterfaceinstabilities
4.6Afirstlookatgravitywaveinstabilities
4.6.1Thesmallamplitudeonsetofwaveinstability
4.6.2Furthernumericalresults
4.7Summary
Exercises
5Modelequationsforsmallamplitudewavesandsolitons;weaklynonlineartheory
5.1Introduction
5.1.1Somephysicalequationsaskforsurgery
5.1.2Examples
5.2Afewmodelequationsasderivedbyintroducingasmall
parameter
5.2.1Shallowwater,weakamplitudegravitywaves
5.2.2Weakamplitudeionacousticwavesinanunmagnetizedplasma
5.2.3Weakamplitudeionacousticwavesinamagnetizedplasma
5.3Weaklynonlinearwaves
5.3.1Spreading,splittingandinstabilities
5.3.2Thestoryofdeepwaterwaves
5.3.3Mysteryofthemissingterm
5.3.4Dynamicsofawavepacket
5.3.5Somegeneralizations
5.4Agenerallookattwofamiliesofmodelequations
5.5AnaturalextensiontofiniteamplitudewavesduetoHayes
5.6Temporaldevelopmentofinstabilitiesandwave-wavecoupling
5.7Concludingremarks
Exercises
6Exactmethodsforfullynonlinearwavesandsolitons
6.1Introduction
6.2Phaseplaneanalysisandothermethods
6.2.1Onestationarywaveinadissipationlessmedium
6.2.2Atwo-fluidlayersolitonpair
6.2.3Weakionacousticshockwavesinacollisionalplasma
6.2.4Solitonsgeneratedbylaserfields
6.2.5Solitonsanddomainsindipolechains
6.2.6Discreteequations
6.3Bernstein-Greene-Kruskalwaves
6.3.1StatisticaldescriptionofaplasmaandBGKwaves
6.3.2Notrappedparticles
6.3.3Variouslimits
6.3.4Trappedparticleequilibria
6.3.5Stability;subsequentdevelopments
6.4Lagrangianmethods
6.5Lagrangianinterpolation
Exercises
7Cartesiansolitonsinoneandtwospacedimensions
7.1Introduction
7.2Thedirectmethod
7.3Constantsofmotion
7.4Inversescatteringmethod
7.5Backlundtransformations
7.6Entr'acte..
7.7Breathersandboundaryeffects
7.8Experimentalevidence
7.9Planesolitoninteractionintwospacedimensions
7.9.1Introducingthetracemethod
7.9.2Oneandtwosotitonsolutions
7.9.3Someotherdevelopmentsandsummary
7.10IntegrableequationsintwospacedimensionsastreatedbytheZakharov-Shabatmethod
7.10.1LaxpairsandthePDEstheyrepresent
7.10.2Extensiontox,y,t
7.10.3HowtoproceedfromtheLaxpairtothegeneralsolution
7.10.4Anexample:theKadomtsev-Petviashviliequation
7.11Summary
Exercises
8Evolutionandstabilityofinitiallyone-dimensionalwavesandsolitons
8.1Abriefhistoricalsurveyoflargeamplitudenonlinearwavestudies
8.1.1Solitons
8.1.2Waterwavesareunstable
8.1.3Thegeometricalopticslimit
8.1.4Morerecentresults
8.1.5WhattheremainderofChapter8isabout
8.2FourmethodsasillustratedbythenonlinearKlein-Gordonequation
8.2.1WhithamI
8.2.2WhithamII
8.2.3Kexpansion
8.2.4Hayes
8.3Higherdimensionaldynamics
8.3.1Kadomtsev-PetviashviliasanalysedbyWhithamII
8.3.2Variouslimits
8.3.3Commonfeaturesoftheweakamplitudeandsolitonlimitsforψ=0
8.3.4Groupvelocity
8.3.5Zakharov-KuznetsovasanalysedbyKexpansion
8.3.6Thevariationalmethod
8.4Amorephysicalapproachleadingtoanassessmentofmodels
8.4.1Formofthewavesconsidered
8.4.2Unmagnetizedplasmas,ftc=0
8.4.3Magnetizedplasmas,Ωc>0
8.5Dynamicsofnonlinearwave,shockandsolitonsolutionstothecubicnonlinearSchrodingerequation
8.5.1Resultsofageneralstabilitycalculation
8.5.2One-dimensionaldynamics:ψ=0
8.5.3Obliqueandperpendicularpropagationofperturbations
8.6ThedirectKmethod
8.6.1TransverseinstabilityofZakharov-Kuznetsovsolitons
8.6.2TheCahn-Hilliardequation
8.7Somegeneralconclusionsandpossiblefuturelinesofinvestigation
Exercises
9Cylindricalandsphericalsolitonsinplasmasandothermedia
9.1Interestinhigherdimensionalplasmasolitons
9.2Unidirectionalcylindricalandsphericalionacousticsolitons
9.2.1Modelequationsinnon-Cartesiangeometry
9.2.2CylindricalsolitonequationsCIandCII
9.2.3Sphericalsolitons
9.2.4Summary
9.3Propertiesofunidirectionalsolitonequations
9.3.1Integrabilitybyinversescattering
9.3.2Conservationlaws
9.4Solitonsolutionsascomparedwithnumericsandexperiments
9.4.1ExactsolutionstoCI
9.4.2Initialvalueproblemandexperiments
9.4.3Reflectionfromtheaxis(centre)
9.4.4Models
9.4.5Stabilityofcylindricalsolitons
9.5Langmuirsolitons
9.5.1Integrability
9.5.2StabilityofLangmuirsolitons
9.6Interactingsolitonsandsomeconclusions
9.7Epilogue.Someotherexamplesofsphericalandcylindricalsolitons
Exercises
10Solitonmetamorphosis
10.1Thenextstepininvestigatingsolitonbehaviour
10.2DecayoflineKPIsolitonsintwodimensions
10.3Decayof2Dsolitonsinthreedimensions
10.3.12Dsolitonsperturbedperpendiculartothemotion
10.3.22Dsolitonsperturbedparalleltothevelocity
10.4Conclusions
Exercises
11Non-coherentphenomena
11.1Introduction
11.2Bifurcationsequencesandchaos
11.3Flowsandmaps
11.4Strangeattractors
11.5Effectofexternalnoise
11.6Experimentalevidenceforstrangeattractors
11.7Othertheoriesofturbulence
11.8Conclusions
Exercises
Appendices
A1Parameterstretchingassuggestedbythelineardispersionrelations
A1.1Ionacousticwavesinanunmagnetizedplasma,Ωc=0
Al.2Magnetizedplasmas,Ωc>0
A2Relationbetweenthetracemethodandtheinversescatteringmethod
A3Someformulaeforperturbednonlinearionacousticwavesandsolitons
A3.1Nomagneticfield
A3.2Ωc>0
A4Collidingsolitontheory
A5Amodelequationforsphericalsolitons
A6Stabilitycalculationfor2DKPIsolitonin3D
References
Authorindex
Subjectindex
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