The Painlevé handbook:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 234-252) and index |
| Beschreibung: | XXIII, 256 S. graph. Darst. |
| ISBN: | 9781402084904 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
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| 008 | 081111s2008 ne d||| |||| 00||| eng d | ||
| 010 | |a 2008926210 | ||
| 020 | |a 9781402084904 |9 978-1-4020-8490-4 | ||
| 020 | |z 9781402084911 |c ebook |9 978-1-4020-8491-1 | ||
| 035 | |a (OCoLC)234147311 | ||
| 035 | |a (DE-599)DNB987990276 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a ne |c NL | ||
| 049 | |a DE-703 |a DE-29T |a DE-91G |a DE-11 | ||
| 050 | 0 | |a QC20.7.D5 | |
| 082 | 0 | |a 518/.6 | |
| 084 | |a SK 500 |0 (DE-625)143243: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a MAT 340f |2 stub | ||
| 100 | 1 | |a Conte, Robert |d 1943- |e Verfasser |0 (DE-588)121614638 |4 aut | |
| 245 | 1 | 0 | |a The Painlevé handbook |c Robert Conte ; Micheline Musette |
| 264 | 1 | |a Dordrecht |b Springer |c 2008 | |
| 300 | |a XXIII, 256 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 234-252) and index | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Painlevé equations | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 0 | 7 | |a Painlevé-Test |0 (DE-588)4344258-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Painlevé-Test |0 (DE-588)4344258-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Musette, Micheline |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016961422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016961422 | ||
Datensatz im Suchindex
| _version_ | 1804138314006003712 |
|---|---|
| adam_text | Contents
Introduction
................................................... 1
1.1
Singularities in the Complex Plane
............................ 1
1.1.1
Perturbative Method
.................................. 2
1.1.2
Nonperturbative Method
.............................. 3
1.2
Painlevé
Property and the Six Transcendents
.................... 6
Singularity Analysis:
Painlevé
Test
............................... 11
2.1
Kowalevski-Gambier Method
................................ 11
2.1.1
LorenzModel
....................................... 12
2.1.2
Kuramoto-Sivashinsky (KS) Equation
................... 16
2.1.3
Cubic Complex
Ginzburg-Landau (CGL3)
Equation
...... 19
2.1.4
Duffing-van
der Pol
Oscillator
......................... 21
2.1.5
Hénon-Heiles
System
................................ 23
2.2
Fuchsian Perturbative Method
................................ 28
2.3
NonFuchsian Perturbative Method
............................ 31
Integrating Ordinary Differential Equations
...................... 33
3.1
Integrable
Situation
......................................... 34
3.1.1
First Integrals and Integration of the
Lorenz
Model
........ 34
3.1.1.1
Case
(1,1/2,0).............................. 35
3.1.1.2
Case
(2,1,1/9).............................. 36
3.1.1.3
Case
(0,1/3,/·).............................. 37
3.1.1.4
Case
(1,0,/·)................................ 37
3.1.2
General Traveling Wave of KdV Equation
............... 38
3.1.3
General Traveling Wave of NLS Equation
................ 40
3.2
Partially
Integrable
Situation
................................. 44
3.2.1
Traveling Wave Reduction of KS and CGL3
.............. 44
3.2.1.1
Nonexistence of a First Integral
................ 45
3.2.1.2
Counting of the Arbitrary Constants
............ 45
3.2.2
Elliptic Traveling Waves
.............................. 47
3.2.2.1
Necessary Conditions for Elliptic Solutions
...... 48
Contents
3.2.2.2
The Elliptic Solutions
........................ 49
3.2.3
Trigonometric Traveling Waves of KS
................... 51
3.2.3.1
Gauge Transformation
........................ 51
3.2.3.2
Polynomials in tanh
.......................... 52
3.2.4
Trigonometric Traveling Waves of CGL3
................ 55
3.2.4.1
Polynomials in tanh
.......................... 57
3.2.4.2
Polynomials in tanh and sech
.................. 60
3.2.5
General Method to Find Elliptic Traveling Waves
......... 63
3.2.5.1
Application to KdV
.......................... 67
3.2.5.2
Application to KS
............................ 68
3.2.5.3
Application to CGL3
......................... 69
3.2.6
First Integral of the Duffing-van
der Pol
Oscillator
........ 71
3.2.7
Singlevalued Solutions of the
Bianchi
IX Cosmological
Model
.............................................. 72
3.2.8
Results of the Nevanlinna Theory on KS and CGL3
....... 74
Partial Differential Equations:
Painlevé Test
...................... 77
4.1
On Reductions
............................................. 78
4.2
Soliton Equations
.......................................... 80
4.3
Painlevé
Property for PDEs
.................................. 82
4.4
Painlevé Test
.............................................. 85
4.4.1
Optimal Expansion Variable
........................... 85
4.4.2
Integrable
Situation, Example of KdV
................... 87
4.4.3
Partially
Integrable
Situation, Example of KPP
........... 89
From the Test to Explicit Solutions of PDEs
....................... 93
5.1
Global Information from the Test
............................. 93
5.2
Building W-Soliton Solutions
................................. 94
5.3
Tools of Integrability
........................................ 94
5.3.1
Lax Pair
............................................ 95
5.3.2
Darboux Transformation
.............................. 97
5.3.3
Crum Transformation
................................. 99
5.3.4
Singular Part Transformation
..........................100
5.3.5
Nonlinear Superposition Formula
.......................101
5.4
Choosing the Order of Lax Pairs
..............................103
5.4.1
Second-Order Lax Pairs and Their Privilege
..............103
5.4.2
Third-Order Lax Pairs
................................104
5.5
Singular Manifold Method
...................................105
5.5.1
Algorithm
..........................................105
5.5.2
Level of Truncation and Choice of Variable
..............107
5.6
Application to
Integrable
Equations
...........................109
5.6.1
One-Family Cases: KdV and Boussinesq
................110
5.6.1.1
TheCase of KdV
............................110
5.6.1.2
The Case of Boussinesq
.......................113
5.6.2
Two-Family Cases: Sine-Gordon and Modified KdV
.......116
Contents xix
5.6.2.1
The Sine-Gordon Equation
....................117
5.6.2.2
The Modified Korteweg-de
Vries
Equation
......120
5.6.3
Third Order: Sawada-Kotera and Kaup-Kupershmidt
......122
5.6.3.1
Help from the
Gambier
Classification
...........123
5.6.3.2
Singularity Structure of SK and KK Equations
.... 124
5.6.3.3
Truncation with a Second Order Lax Pair
........126
5.6.3.4
Truncation with a Third Order Lax Pair and G5
... 127
5.6.3.5
Truncation with a Third Order Lax Pair and G25
.. 127
5.6.3.6
Bäcklund
Transformation
.....................127
5.6.3.7
Nonlinear Superposition Formula
...............128
5.7
Application to Partially
Integrable
Equations
....................130
5.7.1
One-Family Case: Fisher Equation
......................130
5.7.2
Two-Family Case: KPP Equation
.......................133
5.8
Reduction of the Singular Manifold Method to the ODE Case
.....136
5.8.1
From Lax Pair to Isomonodromic Deformation
...........137
5.8.2
From
ВТ
to
Birational
Transformation
..................139
5.8.3
From NLSF to Contiguity Relation
.....................141
5.8.4
Reformulation of the Singular Manifold Method: an
Additional Homography
..............................143
6
Integration of Hamiltonian Systems
..............................145
6.1
Various Integrations
........................................145
6.2
Cubic
Hénon-Heiles Hamiltonians
............................146
6.2.1
Second Invariants
....................................146
6.2.2
Separation of Variables
...............................147
6.2.2.1
Case
β/α
= -6
(KdV5)
......................147
6.2.2.2
Cases
β/α
= -1
(SK) and
-16
(KK)
...........148
6.2.3
Direct Integration
....................................151
6.3
Quartic
Hénon-Heiles
Hamiltonians
...........................153
6.3.1
Second Invariants
....................................153
6.3.2
Separation of Variables
...............................154
6.3.2.1
Case
1:2:1
(Manakov System)
.................154
6.3.2.2
Cases
1:6:1
and
1:6:8.........................155
6.3.2.3
Case
1:12:16................................158
6.3.3
Painlevé
Property
....................................160
6.4
Final Picture for HH3 and HH4
...............................162
7
Discrete Nonlinear Equations
....................................163
7.1
Generalities
...............................................163
7.2
Discrete
Painlevé
Property
...................................166
7.3
Discrete
Painlevé
Test
.......................................167
7.3.1
Method of Singularity Confinement
.....................167
7.3.2
Method of Polynomial Growth
.........................170
7.3.3
Method of Perturbation of the Continuum Limit
..........172
7.4
Discrete Riccati Equation
....................................174
xx Contents
7.5
Discrete
Lax
Pairs
..........................................175
7.6
Exact Discretizations
.......................................177
7.6.1
Ermakov-Pinney Equation
............................177
7.6.2
Elliptic Equation
.....................................180
7.7
Discrete Versions of NLS
....................................181
7.8
A Sketch of Discrete
Painlevé
Equations
.......................182
7.8.1
Analytic Approach
...................................183
7.8.2
Geometric Approach
.................................184
7.8.3
Summary of Discrete
Painlevé
Equations
................185
8
FAQ (Frequently Asked Questions)
...............................187
Appendix A The Classical Results of
Painlevé
and Followers
...........191
A.
1
Groups of
Invariance
of the
Painlevé
Property
...................192
A.
2
Irreducibility. Classical Solutions
.............................193
A.3 Classifications
.............................................194
A.3.1 First Order Higher Degree ODEs
.......................194
A.3.2 Second Order First Degree ODEs
.......................195
A.3.3 Second Order Higher Degree ODEs
.....................196
A.3.4 Third Order First Degree ODEs
........................196
A.3.5 Fourth Order First Degree ODEs
.......................196
A.3.6 HigherOrder First Degree ODEs
.......................198
A.3.7 Second Order First Degree PDEs
.......................198
Appendix
В
More on the
Painlevé
Transcendents
.....................199
B.
1
Coalescence Cascade
.......................................200
B.2
Invariance
Under
Homographies
..............................203
B.3
Invariance
Under
Birational
Transformations
...................204
B.3.1 Normal Sequence
....................................204
B.3.2 Biased Sequence
.....................................206
B.4
Invariance
Under
Affine Weyl
Groups
.........................207
B.5
Invariance
Under Nonbirational Transformations
................209
B.6 Hamiltonian Structure
.......................................209
B.7 Lax Pairs
.................................................210
B.8 Classical Solutions
.........................................212
Appendix
С
Brief Presentation of the Elliptic Functions
...............215
C.I The Notation of Jacobi and
Weierstrass
........................216
C.2 The Symmetric Notation of
Halphen
..........................217
Appendix
D
Basic Introduction to the Nevanlinna Theory
.............219
Appendix
E
The Bilinear Formalism
................................223
E.I Bilinear Representation of a PDE
.............................223
E.2 Bilinear Representation of
a Bäcklund
Transformation
...........225
Contents xxi
Appendix
F
Algorithm for Computing Laurent Series
................229
References
.........................................................234
Index
.............................................................253
|
| adam_txt |
Contents
Introduction
. 1
1.1
Singularities in the Complex Plane
. 1
1.1.1
Perturbative Method
. 2
1.1.2
Nonperturbative Method
. 3
1.2
Painlevé
Property and the Six Transcendents
. 6
Singularity Analysis:
Painlevé
Test
. 11
2.1
Kowalevski-Gambier Method
. 11
2.1.1
LorenzModel
. 12
2.1.2
Kuramoto-Sivashinsky (KS) Equation
. 16
2.1.3
Cubic Complex
Ginzburg-Landau (CGL3)
Equation
. 19
2.1.4
Duffing-van
der Pol
Oscillator
. 21
2.1.5
Hénon-Heiles
System
. 23
2.2
Fuchsian Perturbative Method
. 28
2.3
NonFuchsian Perturbative Method
. 31
Integrating Ordinary Differential Equations
. 33
3.1
Integrable
Situation
. 34
3.1.1
First Integrals and Integration of the
Lorenz
Model
. 34
3.1.1.1
Case
(1,1/2,0). 35
3.1.1.2
Case
(2,1,1/9). 36
3.1.1.3
Case
(0,1/3,/·). 37
3.1.1.4
Case
(1,0,/·). 37
3.1.2
General Traveling Wave of KdV Equation
. 38
3.1.3
General Traveling Wave of NLS Equation
. 40
3.2
Partially
Integrable
Situation
. 44
3.2.1
Traveling Wave Reduction of KS and CGL3
. 44
3.2.1.1
Nonexistence of a First Integral
. 45
3.2.1.2
Counting of the Arbitrary Constants
. 45
3.2.2
Elliptic Traveling Waves
. 47
3.2.2.1
Necessary Conditions for Elliptic Solutions
. 48
Contents
3.2.2.2
The Elliptic Solutions
. 49
3.2.3
Trigonometric Traveling Waves of KS
. 51
3.2.3.1
Gauge Transformation
. 51
3.2.3.2
Polynomials in tanh
. 52
3.2.4
Trigonometric Traveling Waves of CGL3
. 55
3.2.4.1
Polynomials in tanh
. 57
3.2.4.2
Polynomials in tanh and sech
. 60
3.2.5
General Method to Find Elliptic Traveling Waves
. 63
3.2.5.1
Application to KdV
. 67
3.2.5.2
Application to KS
. 68
3.2.5.3
Application to CGL3
. 69
3.2.6
First Integral of the Duffing-van
der Pol
Oscillator
. 71
3.2.7
Singlevalued Solutions of the
Bianchi
IX Cosmological
Model
. 72
3.2.8
Results of the Nevanlinna Theory on KS and CGL3
. 74
Partial Differential Equations:
Painlevé Test
. 77
4.1
On Reductions
. 78
4.2
Soliton Equations
. 80
4.3
Painlevé
Property for PDEs
. 82
4.4
Painlevé Test
. 85
4.4.1
Optimal Expansion Variable
. 85
4.4.2
Integrable
Situation, Example of KdV
. 87
4.4.3
Partially
Integrable
Situation, Example of KPP
. 89
From the Test to Explicit Solutions of PDEs
. 93
5.1
Global Information from the Test
. 93
5.2
Building W-Soliton Solutions
. 94
5.3
Tools of Integrability
. 94
5.3.1
Lax Pair
. 95
5.3.2
Darboux Transformation
. 97
5.3.3
Crum Transformation
. 99
5.3.4
Singular Part Transformation
.100
5.3.5
Nonlinear Superposition Formula
.101
5.4
Choosing the Order of Lax Pairs
.103
5.4.1
Second-Order Lax Pairs and Their Privilege
.103
5.4.2
Third-Order Lax Pairs
.104
5.5
Singular Manifold Method
.105
5.5.1
Algorithm
.105
5.5.2
Level of Truncation and Choice of Variable
.107
5.6
Application to
Integrable
Equations
.109
5.6.1
One-Family Cases: KdV and Boussinesq
.110
5.6.1.1
TheCase of KdV
.110
5.6.1.2
The Case of Boussinesq
.113
5.6.2
Two-Family Cases: Sine-Gordon and Modified KdV
.116
Contents xix
5.6.2.1
The Sine-Gordon Equation
.117
5.6.2.2
The Modified Korteweg-de
Vries
Equation
.120
5.6.3
Third Order: Sawada-Kotera and Kaup-Kupershmidt
.122
5.6.3.1
Help from the
Gambier
Classification
.123
5.6.3.2
Singularity Structure of SK and KK Equations
. 124
5.6.3.3
Truncation with a Second Order Lax Pair
.126
5.6.3.4
Truncation with a Third Order Lax Pair and G5
. 127
5.6.3.5
Truncation with a Third Order Lax Pair and G25
. 127
5.6.3.6
Bäcklund
Transformation
.127
5.6.3.7
Nonlinear Superposition Formula
.128
5.7
Application to Partially
Integrable
Equations
.130
5.7.1
One-Family Case: Fisher Equation
.130
5.7.2
Two-Family Case: KPP Equation
.133
5.8
Reduction of the Singular Manifold Method to the ODE Case
.136
5.8.1
From Lax Pair to Isomonodromic Deformation
.137
5.8.2
From
ВТ
to
Birational
Transformation
.139
5.8.3
From NLSF to Contiguity Relation
.141
5.8.4
Reformulation of the Singular Manifold Method: an
Additional Homography
.143
6
Integration of Hamiltonian Systems
.145
6.1
Various Integrations
.145
6.2
Cubic
Hénon-Heiles Hamiltonians
.146
6.2.1
Second Invariants
.146
6.2.2
Separation of Variables
.147
6.2.2.1
Case
β/α
= -6
(KdV5)
.147
6.2.2.2
Cases
β/α
= -1
(SK) and
-16
(KK)
.148
6.2.3
Direct Integration
.151
6.3
Quartic
Hénon-Heiles
Hamiltonians
.153
6.3.1
Second Invariants
.153
6.3.2
Separation of Variables
.154
6.3.2.1
Case
1:2:1
(Manakov System)
.154
6.3.2.2
Cases
1:6:1
and
1:6:8.155
6.3.2.3
Case
1:12:16.158
6.3.3
Painlevé
Property
.160
6.4
Final Picture for HH3 and HH4
.162
7
Discrete Nonlinear Equations
.163
7.1
Generalities
.163
7.2
Discrete
Painlevé
Property
.166
7.3
Discrete
Painlevé
Test
.167
7.3.1
Method of Singularity Confinement
.167
7.3.2
Method of Polynomial Growth
.170
7.3.3
Method of Perturbation of the Continuum Limit
.172
7.4
Discrete Riccati Equation
.174
xx Contents
7.5
Discrete
Lax
Pairs
.175
7.6
Exact Discretizations
.177
7.6.1
Ermakov-Pinney Equation
.177
7.6.2
Elliptic Equation
.180
7.7
Discrete Versions of NLS
.181
7.8
A Sketch of Discrete
Painlevé
Equations
.182
7.8.1
Analytic Approach
.183
7.8.2
Geometric Approach
.184
7.8.3
Summary of Discrete
Painlevé
Equations
.185
8
FAQ (Frequently Asked Questions)
.187
Appendix A The Classical Results of
Painlevé
and Followers
.191
A.
1
Groups of
Invariance
of the
Painlevé
Property
.192
A.
2
Irreducibility. Classical Solutions
.193
A.3 Classifications
.194
A.3.1 First Order Higher Degree ODEs
.194
A.3.2 Second Order First Degree ODEs
.195
A.3.3 Second Order Higher Degree ODEs
.196
A.3.4 Third Order First Degree ODEs
.196
A.3.5 Fourth Order First Degree ODEs
.196
A.3.6 HigherOrder First Degree ODEs
.198
A.3.7 Second Order First Degree PDEs
.198
Appendix
В
More on the
Painlevé
Transcendents
.199
B.
1
Coalescence Cascade
.200
B.2
Invariance
Under
Homographies
.203
B.3
Invariance
Under
Birational
Transformations
.204
B.3.1 Normal Sequence
.204
B.3.2 Biased Sequence
.206
B.4
Invariance
Under
Affine Weyl
Groups
.207
B.5
Invariance
Under Nonbirational Transformations
.209
B.6 Hamiltonian Structure
.209
B.7 Lax Pairs
.210
B.8 Classical Solutions
.212
Appendix
С
Brief Presentation of the Elliptic Functions
.215
C.I The Notation of Jacobi and
Weierstrass
.216
C.2 The Symmetric Notation of
Halphen
.217
Appendix
D
Basic Introduction to the Nevanlinna Theory
.219
Appendix
E
The Bilinear Formalism
.223
E.I Bilinear Representation of a PDE
.223
E.2 Bilinear Representation of
a Bäcklund
Transformation
.225
Contents xxi
Appendix
F
Algorithm for Computing Laurent Series
.229
References
.234
Index
.253 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Conte, Robert 1943- Musette, Micheline |
| author_GND | (DE-588)121614638 |
| author_facet | Conte, Robert 1943- Musette, Micheline |
| author_role | aut aut |
| author_sort | Conte, Robert 1943- |
| author_variant | r c rc m m mm |
| building | Verbundindex |
| bvnumber | BV035154216 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.D5 |
| callnumber-search | QC20.7.D5 |
| callnumber-sort | QC 220.7 D5 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 500 SK 950 |
| classification_tum | MAT 340f |
| ctrlnum | (OCoLC)234147311 (DE-599)DNB987990276 |
| dewey-full | 518/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.6 |
| dewey-search | 518/.6 |
| dewey-sort | 3518 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035154216 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:48:01Z |
| indexdate | 2024-07-09T21:26:13Z |
| institution | BVB |
| isbn | 9781402084904 |
| language | English |
| lccn | 2008926210 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016961422 |
| oclc_num | 234147311 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-703 DE-29T DE-91G DE-BY-TUM DE-11 |
| physical | XXIII, 256 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Conte, Robert 1943- Verfasser (DE-588)121614638 aut The Painlevé handbook Robert Conte ; Micheline Musette Dordrecht Springer 2008 XXIII, 256 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 234-252) and index Mathematische Physik Painlevé equations Mathematical physics Painlevé-Test (DE-588)4344258-4 gnd rswk-swf Painlevé-Test (DE-588)4344258-4 s DE-604 Musette, Micheline Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016961422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conte, Robert 1943- Musette, Micheline The Painlevé handbook Mathematische Physik Painlevé equations Mathematical physics Painlevé-Test (DE-588)4344258-4 gnd |
| subject_GND | (DE-588)4344258-4 |
| title | The Painlevé handbook |
| title_auth | The Painlevé handbook |
| title_exact_search | The Painlevé handbook |
| title_exact_search_txtP | The Painlevé handbook |
| title_full | The Painlevé handbook Robert Conte ; Micheline Musette |
| title_fullStr | The Painlevé handbook Robert Conte ; Micheline Musette |
| title_full_unstemmed | The Painlevé handbook Robert Conte ; Micheline Musette |
| title_short | The Painlevé handbook |
| title_sort | the painleve handbook |
| topic | Mathematische Physik Painlevé equations Mathematical physics Painlevé-Test (DE-588)4344258-4 gnd |
| topic_facet | Mathematische Physik Painlevé equations Mathematical physics Painlevé-Test |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016961422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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