The Painlevé property: one century later
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg
Springer
1999
|
| Schriftenreihe: | CRM series in mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XXVI, 810 S. Ill., graph. Darst. |
| ISBN: | 0387988882 |
Internformat
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| 245 | 1 | 0 | |a The Painlevé property |b one century later |c Robert Conte ed. |
| 264 | 1 | |a New York ; Berlin ; Heidelberg |b Springer |c 1999 | |
| 300 | |a XXVI, 810 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a CRM series in mathematical physics | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Painlevé, Équations de | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Painlevé equations | |
| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Analytische Lösung |0 (DE-588)4313842-1 |D s |
| 689 | 0 | 2 | |a Painlevé-Test |0 (DE-588)4344258-4 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008806299 | ||
Datensatz im Suchindex
| _version_ | 1804127624573747200 |
|---|---|
| adam_text | Contents
Participants ix
Series Preface xiii
Preface xv
Contributors xxv
1 Singularities of Ordinary Linear Differential Equations and
Integrability 1
Jean Reignier
1 Generalities 1
2 Structure of the Solutions of the Homogeneous Equation
Around an Isolated Singular Point 6
3 Weakly Singular Equations (Fuchs) 12
4 Thome s Equations 22
5 Global Considerations 27
6 References 32
2 Introduction to the Theory of Isomonodromic
Deformations of Linear Ordinary Differential Equations
with Rational Coefficients 35
Gilbert Mahoux
1 Introduction 35
2 Isomonodromic Deformations of Linear ODEs with Fuchsian
Singularities 38
3 The Isomonodromic Deformation Problem for Painleve VI .. 46
4 Isomonodromic Deformations of Linear ODEs with Thome
Singularities 52
5 An Isomonodromic Deformation Problem for Painleve I ... 63
6 Conclusion 68
7 Appendix A: Matrix Versus Scalar Formalisms and Fuchs s
Theorem 70
8 Appendix B: Asymptotic Power Series 73
9 References 74
3 The Painleve Approach to Nonlinear Ordinary Differential
Equations 77
xx Contents
Robert Conte
1 Introduction 77
2 The Meromorphy Assumption 83
3 The True Problems 96
4 The Classical Results (L. Puchs, Poincare, Painleve) 105
5 Construction of Necessary Conditions. The Theory 108
6 Construction of Necessary Conditions. The Painleve Test ... 153
7 Sufficiency: Explicit Integration Methods 164
8 Conclusion 171
9 References 172
4 Asymptotic Studies of the Painleve Equations 181
Nalini Joshi
1 Introduction 181
2 Linear and Nonlinear Asymptotic Models 192
3 The First and Second Painleve Equations 205
4 Global Extensions 217
5 Conclusion 223
6 References 224
5 2 D Quantum and Topological Gravities, Matrix Models,
and Integrable Differential Systems 229
Philippe Di Francesco
Part A 2 D Quantum Gravity 229
1 Introduction 229
2 The One Matrix Model: Large N Limit 238
3 The One Matrix Model: Exact Solution 246
4 The Double Scaling Limit 251
5 Multimatrix Models 261
6 Conclusion 269
Part B 2 D Topological Gravity 270
7 Introduction 270
8 Computing the Kontsevich Integral 273
9 The Kontsevich Integral as r Function of the KdV Hierarchy . 278
10 Main Equivalence Theorem Between Topological and
Quantum Gravities 280
11 Conclusion 283
12 References 283
6 Painleve Transcendents in Two Dimensional Topological
Field Theory 287
Boris Dvbrovin
1 Algebraic Properties of Correlators in 2 D Topological Field
Theories. Moduli of a 2 D TFT and WDVV Equations of
Associativity 288
Contents xxi
2 Equations of Associativity and Frobenius Manifolds. Deformed
Flat Connection and Its Monodromy at the Origin 300
3 Semisimplicity and Canonical Coordinates 333
4 Stokes Matrices and Classification of Semisimple Frobenius
Manifolds 344
5 Monodromy Group and Mirror Construction for Semisimple
Frobenius Manifolds 379
6 References 406
7 Discrete Painleve Equations 413
Basile Grammaticos, Frank W. Nijhoff, and Alfred Ramani
Introduction 413
1 Integrable Discrete Systems 416
2 Similarity Reduction and Direct Linearization 432
3 The Painleve Property for Discrete Systems 455
4 Properties of the Discrete Painleve Equations 476
5 Monodromy Problems and ^ Difference Equations 486
6 References 505
8 Painleve Analysis for Nonlinear Partial Differential
Equations 517
Micheline Musttte
1 Introduction 517
2 Integrable Equations 519
3 Painleve Analysis for PDEs 535
4 Partially Integrable and Nonintegrable Equations 558
5 References 562
9 On Painleve and Darboux—Halphen Type Equations 573
Mark J. Ablowitz, Sarby Chakravarty, and Rod Halburd
1 Introduction 573
2 Painleve Equations and 1ST 574
3 Darboux Halphen Systems and Their Linear Problems as
Reductions of SDYM 578
4 The Monodromy Evolving System and the Solution of the
Generalized DH System 585
5 Discussion 587
6 References 588
10 Symmetry Reduction and Exact Solutions of Nonlinear
Partial Differential Equations 591
Peter A. Clarkson and Pavel Winternitz
1 Introduction 591
2 Algorithm for Calculating the Symmetry Group of a
Differential System 592
xxii Contents
3 Examples of Symmetry Groups 596
4 Symmetry Reduction, Group Invariant Solutions, Partially
Invariant Solutions 604
5 Classification of the Subalgebras of a Finite Dimensional Lie
Algebra 615
6 Direct Reductions and Conditional Symmetries 623
7 Conclusions 645
8 References 646
11 Painleve Equations in Terms of Entire Functions 661
Jarmo Hietarinta
1 Introduction 661
2 Hirota s Bilinear Method for Soliton Equations 663
3 Bilinear Forms and Similarity Reduction 667
4 Solutions in Terms of Entire Functions 672
5 Discrete Painleve 681
6 References 685
12 Backlund Transformations of Painleve Equations and Their
Applications 687
Valerii I. Gromak
1 Introduction 688
2 The Second Painleve Equation 695
3 Rational Solutions of (P2) (0 Solutions) 700
4 One Parameter Families of Classical Solutions (1 Solutions) . 702
5 Algebraic Nonintegrability of (P2) 703
6 Higher Analogue of (P2) 705
7 The Fourth Painleve Equation 708
8 Classical Solutions of (P4) 712
9 Rational Solutions of (P4) 716
10 The Third Painleve Equation 719
11 Equation (P3) for 7 = 0, a6 ^ 0 722
12 Equation (P3) for 76 ^ 0 724
13 Rational and Classical Solutions of (P3) for 76 ^ 0 727
14 The Fifth Painleve Equation 729
15 The Sixth Painleve Equation 732
16 References 734
13 The Hamiltonians Associated to the Painleve Equations 735
Kazuo Okamoto
1 Introduction 735
2 Hamiltonians and Painleve Analysis 736
3 The Space of Initial Conditions 744
4 The Irreducibility of Pn 753
5 The r Functions of the Second Painleve System 762
Contents xxiii
6 The Painleve System of Two Variables 771
7 References 784
14 Completeness of the Painleve Test—General
Considerations—Open Problems 789
Martin D. Kruskal
1 Cultures in Mathematics 789
2 The Painleve Test 792
3 The PolyPainleve Test 797
4 Asymptotic Expansions 800
5 References 803
Index 805
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| genre_facet | Konferenzschrift 1999 Cargese |
| id | DE-604.BV012933403 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:36:19Z |
| institution | BVB |
| isbn | 0387988882 |
| language | German |
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| physical | XXVI, 810 S. Ill., graph. Darst. |
| publishDate | 1999 |
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| publisher | Springer |
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| series2 | CRM series in mathematical physics |
| spelling | The Painlevé property one century later Robert Conte ed. New York ; Berlin ; Heidelberg Springer 1999 XXVI, 810 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRM series in mathematical physics Literaturangaben Painlevé, Équations de Physique mathématique Mathematische Physik Mathematical physics Painlevé equations Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Analytische Lösung (DE-588)4313842-1 gnd rswk-swf Painlevé-Test (DE-588)4344258-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1999 Cargese gnd-content Nichtlineare Differentialgleichung (DE-588)4205536-2 s Analytische Lösung (DE-588)4313842-1 s Painlevé-Test (DE-588)4344258-4 s DE-604 Conte, Robert 1943- Sonstige (DE-588)121614638 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008806299&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The Painlevé property one century later Painlevé, Équations de Physique mathématique Mathematische Physik Mathematical physics Painlevé equations Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Analytische Lösung (DE-588)4313842-1 gnd Painlevé-Test (DE-588)4344258-4 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4313842-1 (DE-588)4344258-4 (DE-588)1071861417 |
| title | The Painlevé property one century later |
| title_auth | The Painlevé property one century later |
| title_exact_search | The Painlevé property one century later |
| title_full | The Painlevé property one century later Robert Conte ed. |
| title_fullStr | The Painlevé property one century later Robert Conte ed. |
| title_full_unstemmed | The Painlevé property one century later Robert Conte ed. |
| title_short | The Painlevé property |
| title_sort | the painleve property one century later |
| title_sub | one century later |
| topic | Painlevé, Équations de Physique mathématique Mathematische Physik Mathematical physics Painlevé equations Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Analytische Lösung (DE-588)4313842-1 gnd Painlevé-Test (DE-588)4344258-4 gnd |
| topic_facet | Painlevé, Équations de Physique mathématique Mathematische Physik Mathematical physics Painlevé equations Nichtlineare Differentialgleichung Analytische Lösung Painlevé-Test Konferenzschrift 1999 Cargese |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008806299&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT conterobert thepainlevepropertyonecenturylater |