非线性物理科学：变换群和李代数（英文版）

图书标准信息

• 作者 [瑞典]伊布拉基莫夫（Ibragimov N.H.） 著
• 出版社 高等教育出版社
• 出版时间 2013-02
• 版次 1
• ISBN 9787040367416
• 定价 59.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 185页
• 字数 210千字
• 正文语种 英语
• 丛书 非线性物理科学

【内容简介】

　　《非线性物理科学：变换群和李代数（英文版）》为作者在俄罗斯、美国、南非和瑞典多年讲述变换群和李群分析课程的讲义。书中所讨论的局部李群方法提供了求解非线性微分方程解析解通用且非常有效的方法，而近似变换群可以提高构造含少量参数的微分方程的技巧。《非线性物理科学：变换群和李代数（英文版）》通俗易懂、叙述清晰，并提供丰富的模型，能帮助读者轻松地逐步深入各种主题。

【作者简介】

　　伊布拉基莫夫（Ibragimov，N.H.），教授，瑞士科学家，被公认为是在微分方程对称分析方面世界上最具权威的专家之一。他发起并构建了现代群分析理论，并推动了该理论在多方面的应用。

【目录】

Preface
PartⅠLocalTransformationGroups
1Preliminaries
1.1Changesofframesofreferenceandpointtransformations
1.1.1Translations
1.1.2Rotations
1.1.3Galileantransformation
1.2Introductionoftransformationgroups
1.2.1Definitionsandexamples
1.2.2Differenttypesofgroups
1.3Someusefulgroups
1.3.1Finitecontinuousgroupsonthestraightline
1.3.2Groupsontheplane
1.3.3GroupsinIRn
ExercisestoChapter1
2One-parametergroupsandtheirinvariants
2.1Localgroupsoftransformations
2.1.1Notationanddefinition
2.1.2Groupswritteninacanonicalparameter
2.1.3Infinitesimaltransformationsandgenerators
2.1.4Lieequations
2.1.5Exponentialmap
2.1.6Determinationofacanonicalparameter
2.2Invariants
2.2.1Definitionandinfinitesimaltest
2.2.2Canonicalvariables
2.2.3Constructionofgroupsusingcanonicalvariables
2.2.4Frequentlyusedgroupsintheplane
2.3Invariantequations
2.3.1Definitionandinfinitesimaltest
2.3.2Invariantrepresentationofinvariantmanifolds
2.3.3ProofofTheorem
2.3.4ExamplesonTheorem
ExercisestoChapter2
3Groupsadnuttedbydifferentialequations
3.1Preliminaries
3.1.1Differentialvariablesandfunctions
3.1.2Pointtransformations
3.1.3Frameofdifferentialequations
3.2Ptolongationofgrouptransformations
3.2.10ne-dimensionalcase
3.2.2Prolongationwithseveraldifferentialvariables
3.2.3Generalcase
3.3Prolongationofgroupgenerators
3.3.10ne-dimensionalcase
3.3.2Severaldifferentialvariables
3.3.3Generalcase
3.4Firstdefinitionofsymmetrygroups
3.4.1Definition
3.4.2Examples
3.5Seconddefinitionofsymmetrygroups
3.5.1Definitionanddeterminingequations
3.5.2Determiningequationforsecond-orderODEs
3.5.3Examplesonsolutionofdeterminingequations
ExercisestoChapter3
4Liealgebrasofoperators
4.1Basicdefinitions
4.1.2Propertiesofthecommutator
4.1.3Propertiesofdeterminingequations
4.2Basicproperties
4.2.1Notation
4.2.2Subalgebraandideal
4.2.3Derivedalgebras
4.2.4SolvableLiealgebras
4.3Isomorphismandsimilarity
4.3.1IsomorphicLieakebras
4.3.2SimilarLiealgebras
4.4Low-dimensionalLiealgebras
4.4.10ne-dimensionalalgebras
4.4.2Two-dimensionalalgebrasintheplane
4.4.3Three-dimensionalalgebrasintheplane
4.4.4Three-dimensionalalgebrasinlR3
4.5Liealgebrasandmulti-parametergroups
4.5.1Definitionofmulti-parametergroups
4.5.2Constructionofmulti-parametergroups
5Galoisgroupsviasymmetries
5.1Preliminaries
5.2Symmetriesofalgebraicequations
5.2.1Determiningequation
5.2.2Firstexample
5.2.3Secondexample
5.2.4Thirdexample
5.3ConstructionofGaloisgroups
5.3.1Firstexample
5.3.2Secondexample
5.3.3Thirdexample
5.3.4Concludingremarks
AssignmenttoPartI

PartIIApproximateTransformationGroups
6.1Motivation
6.2AsketchonLietransformationgroups
6.2.10ne-parametertransformationgroups
6.2.2Canonicalparameter
6.2.3GroupgeneratorandLieequations
6.3ApproximateCauchyproblem
6.3.1Notation
6.3.2DefinitionoftheapproximateCauchyproblem
7Approximatetransformations
7.1Approximatetransformationsdefined
7.2Approximateone-parametergroups
7.2.1Introductoryremark
7.2.2Definitionofone-parameterapproximate
7.2.3Generatorofapproximatetransformationgroup
7.3Infinitesimaldescription
7.3.1ApproximateLieequations
7.3.2Approximateexponentialmap
ExercisestoChapter7
8Approximatesymmetries
8.1Definitionofapproximatesymmetries
8.2Calculationofapproximatesymmetries
8.2.1Determiningequations
8.2.2Stablesymmetries
8.2.3Algorithmforcalculation
8.3.2ApproximatecommutatorandLiealgebras
9.1Integrationofequationswithasmallparameterusingapproximatesymmetries
9.1.1Equationhavingnoexactpointsymmetries
9.1.2Utilizationofstablesymmetries
9.2Approximatelyinvariantsolutions
9.2.1Nonlinearwaveequation
9.2.2ApproximatetravellingwavesofKdVequation
9.3Approximateconservationlaws
ExercisestoChapter9
AssignmenttoPartII
Bibliography
Index