Nonlinear symmetries and nonlinear equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1994
|
| Schriftenreihe: | Mathematics and its applications
299 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 258 S. graph. Darst. |
| ISBN: | 079233048X |
Internformat
MARC
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| 100 | 1 | |a Gaeta, Giuseppe |d 1959- |e Verfasser |0 (DE-588)121404188 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear symmetries and nonlinear equations |c by Giuseppe Gaeta |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1994 | |
| 300 | |a XIX, 258 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 299 | |
| 650 | 4 | |a Bifurcation | |
| 650 | 4 | |a Equation Einstein | |
| 650 | 4 | |a Equation Fokker-Planck | |
| 650 | 4 | |a Equation Landau-Ginzburg | |
| 650 | 4 | |a Equation Navier-Stokes | |
| 650 | 4 | |a Equation Schrödinger | |
| 650 | 4 | |a Equation Yang-Mills | |
| 650 | 4 | |a Equation non linéaire | |
| 650 | 4 | |a Equation évolution | |
| 650 | 4 | |a Jauge | |
| 650 | 4 | |a Lemme branchement | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Problème variationnel | |
| 650 | 4 | |a Réseau Toda | |
| 650 | 4 | |a Solution périodique | |
| 650 | 4 | |a Symétrie non linéaire | |
| 650 | 7 | |a Symétrie |2 ram | |
| 650 | 4 | |a Système dynamique | |
| 650 | 7 | |a Théories non linéaires |2 ram | |
| 650 | 7 | |a Équations différentielles non linéaires |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Symmetry | |
| 650 | 0 | 7 | |a Nichtlineare algebraische Gleichung |0 (DE-588)4298314-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Symmetrie |0 (DE-588)4058724-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |D s |
| 689 | 0 | 1 | |a Symmetrie |0 (DE-588)4058724-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtlineare algebraische Gleichung |0 (DE-588)4298314-9 |D s |
| 689 | 1 | 1 | |a Symmetrie |0 (DE-588)4058724-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Mathematics and its applications |v 299 |w (DE-604)BV008163334 |9 299 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006512569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006512569 | ||
Datensatz im Suchindex
| _version_ | 1804124192048676864 |
|---|---|
| adam_text | Table of Contents
List of abbreviations zi
Foreword mi
Introduction xvii
Chapter I Geometric getting
Introduction 1
a): Equations and functions as geometrical objects
1. The jet space 2
2. Contact structure of jet space 4
3. Differential equations, solutions, integral manifolds 6
4. The group Diff(M) and its algebra 9
5. The groups Diff(M ro ) and Di// m)(M) 10
6. Group action on algebraic functions and their symmetry 11
7. Group action on prolonged functions and the prolongation formula 12
b): Symmetry
8. Symmetries of algebraic equations 13
9. Symmetries of differential equations 14
10. Symmetry of A versus symmetry of A = 0 15
11. Algebras and prolonged algebras 16
12. Module structure of symmetry of algebraic equations and first order ODEs 17
vi TABLE OF CONTENTS
13. Summary of gioups, algebras, and relations 19
References 21
Chapter II Symmetries and their use
Introduction 23
1. Symmetry of a given equation 24
2. Linear and C linearizable equations 26
3. Equations with a given symmetry 28
4. Canonical coordinates 31
5. Symmetry and reduction of algebraic equations 33
6. Symmetry and reduction of ODEs 36
7. Symmetry and symmetric solutions of PDEs 38
8. Conditional symmetries 40
9. Conditional symmetries and boundary conditions 40
References 43
Chapter HI Examples
Introduction 45
1. Symmetry of algebraic equations 45
2. Symmetry of ODEs (one soliton KdV) 47
3. Symmetry of evolution PDEs (the heat equation) 49
4. Table of prolongations for ODEs 52
5. Table of prolongations for PDEs 53
Chapter IV Evolution equations
Introduction 55
a): Evolution equations genera] features
1. Evolution equations 56
TABLE OF CONTENTS vii
2. Special classes of symmetiies 58
3. Contact tiansfotmations 59
4. Autonomous equations 60
b): Dynamical systems (ODEs)
5. First order ODEs 61
6. Autonomous equations, tangent bundle versus jet space, topology of solutions,
and time independent symmetries 62
7. Equations in Lax form 64
8. Second order ODEs 66
9. Lagrange versus Hamilton equations 68
10. Potential systems 70
11. Higher order ODEs 71
c): Periodic solutions
12. Periodic solutions of autonomous dynamical systems 72
13. Periodic solutions of potential systems 74
14. Point particles on the circle 75
d): Evolution PDEs
15. First order PDEs 76
16. Higher order evolution equations 78
17. Scalar equations linear in higher derivatives 79
18. Equations linear in higher derivatives 80
References 81
Chapter V Variational problems
Introduction 83
1. Variational symmetries and variational problems 84
viii TABLE OF CONTENTS
2. Variations! symmetries and conservation laws:
Lagrangian mechanics and Noether theorem 86
3. Conserved quantities for higher order variational problems: the general Noether theorem 88
4. Noether theorem and divergence symmetries 90
5. Variational symmetries and reduction of order 91
6. Variational symmetries, conservation laws, and the Noether theorem
for infinite dimensional variational problems 92
References 95
Chapter VI Bifurcation problems
Introduction 97
1. Bifurcation problems: general setting 98
2. Bifurcation theory and linear symmetry 99
3. Lie point symmetries and bifurcation 104
4. Symmetries of systems of ODEs depending on a parameter 112
5. Bifurcation points and symmetry algebra 117
6. Extensions 119
References 120
Chapter VH Gauge theories
Introduction 123
1. Symmetry breaking in potential problems and gauge theories 124
2. Strata in RN 126
3. Michel s theorem 127
4. Zero th order gauge functional 129
5. Discussion 131
6. First order gauge functional 132
7. Geometry and stratification of Q 137
8. Stratification of gauge orbit space 139
9. Maximal strata in gauge orbit space 142
TABLE OF CONTENTS ix
10. The equivatiant blanching lemma 144
11. A reduction lemma for gauge invariant potentials 146
12. Some examples of reduction 148
13. Base space symmetries 149
14. A scenario for pattern formation 151
15. A scenario for phase coexistence 152
References 153
Chapter VIII Reduction and equivariant branching lemma
Introduction 155
1. General setting (ODEs) 156
2. The reduction lemma 157
3. The equivariant branching lemma 158
4. General setting (PDEs) 160
5. Gauge symmetries and Lie point vector fields 161
6. Reduction lemma for gauge theories 162
7. Symmetric critical sections of gauge functionals 165
8. Equivariant branching lemma for gauge functionals 165
9. Evolution PDEs 167
10. Symmetries of evolution PDEs 168
11. Reduction lemma for evolution PDEs 171
References 172
Chapter IX Further developements
Introduction 175
1. Missing sections 176
2. Non Linear Superposition Principles 177
3. Symmetry and integrability second order ODEs 180
4. Infinite dimensional (and Kac Moody) Lie point symmetry algebras 180
x TABLE OF CONTENTS
5. Symmetry classification of ODEs 183
6. The Lie determinant 185
7. Systems of lineal second order ODEs 187
8. Cohomology and symmetry of differential equations 189
9. Contact symmetries of evolution equations 192
10. Conditional symmetries, and Boussinesq equation 194
11. Lie point symmetries and maps 197
References 200
Chapter X Equations of Physics
Introduction 205
1. Fokker Planck type equations 206
2. Schroedinger equation for atoms and molecules 208
3. Einstein (vacuum) field equations 209
4. Landau Ginzburg equation 210
5. The $6 field theory (three dimensional Landau Ginzburg equation) 212
6. An equation arising in plasma physics 214
7. Navier Stokes equations 215
8. Yang Mills equations 216
9. Lattice equations and the Toda lattice 218
References 220
References and bibliography 223
Subject Index 253
|
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| id | DE-604.BV009835517 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:45Z |
| institution | BVB |
| isbn | 079233048X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006512569 |
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| owner_facet | DE-12 DE-703 DE-11 DE-188 |
| physical | XIX, 258 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Gaeta, Giuseppe 1959- Verfasser (DE-588)121404188 aut Nonlinear symmetries and nonlinear equations by Giuseppe Gaeta Dordrecht [u.a.] Kluwer 1994 XIX, 258 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 299 Bifurcation Equation Einstein Equation Fokker-Planck Equation Landau-Ginzburg Equation Navier-Stokes Equation Schrödinger Equation Yang-Mills Equation non linéaire Equation évolution Jauge Lemme branchement Physique mathématique ram Problème variationnel Réseau Toda Solution périodique Symétrie non linéaire Symétrie ram Système dynamique Théories non linéaires ram Équations différentielles non linéaires ram Mathematische Physik Differential equations, Nonlinear Mathematical physics Nonlinear theories Symmetry Nichtlineare algebraische Gleichung (DE-588)4298314-9 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Symmetrie (DE-588)4058724-1 s DE-604 Nichtlineare algebraische Gleichung (DE-588)4298314-9 s Mathematics and its applications 299 (DE-604)BV008163334 299 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006512569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gaeta, Giuseppe 1959- Nonlinear symmetries and nonlinear equations Mathematics and its applications Bifurcation Equation Einstein Equation Fokker-Planck Equation Landau-Ginzburg Equation Navier-Stokes Equation Schrödinger Equation Yang-Mills Equation non linéaire Equation évolution Jauge Lemme branchement Physique mathématique ram Problème variationnel Réseau Toda Solution périodique Symétrie non linéaire Symétrie ram Système dynamique Théories non linéaires ram Équations différentielles non linéaires ram Mathematische Physik Differential equations, Nonlinear Mathematical physics Nonlinear theories Symmetry Nichtlineare algebraische Gleichung (DE-588)4298314-9 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4298314-9 (DE-588)4205536-2 (DE-588)4058724-1 |
| title | Nonlinear symmetries and nonlinear equations |
| title_auth | Nonlinear symmetries and nonlinear equations |
| title_exact_search | Nonlinear symmetries and nonlinear equations |
| title_full | Nonlinear symmetries and nonlinear equations by Giuseppe Gaeta |
| title_fullStr | Nonlinear symmetries and nonlinear equations by Giuseppe Gaeta |
| title_full_unstemmed | Nonlinear symmetries and nonlinear equations by Giuseppe Gaeta |
| title_short | Nonlinear symmetries and nonlinear equations |
| title_sort | nonlinear symmetries and nonlinear equations |
| topic | Bifurcation Equation Einstein Equation Fokker-Planck Equation Landau-Ginzburg Equation Navier-Stokes Equation Schrödinger Equation Yang-Mills Equation non linéaire Equation évolution Jauge Lemme branchement Physique mathématique ram Problème variationnel Réseau Toda Solution périodique Symétrie non linéaire Symétrie ram Système dynamique Théories non linéaires ram Équations différentielles non linéaires ram Mathematische Physik Differential equations, Nonlinear Mathematical physics Nonlinear theories Symmetry Nichtlineare algebraische Gleichung (DE-588)4298314-9 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Bifurcation Equation Einstein Equation Fokker-Planck Equation Landau-Ginzburg Equation Navier-Stokes Equation Schrödinger Equation Yang-Mills Equation non linéaire Equation évolution Jauge Lemme branchement Physique mathématique Problème variationnel Réseau Toda Solution périodique Symétrie non linéaire Symétrie Système dynamique Théories non linéaires Équations différentielles non linéaires Mathematische Physik Differential equations, Nonlinear Mathematical physics Nonlinear theories Symmetry Nichtlineare algebraische Gleichung Nichtlineare Differentialgleichung Symmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006512569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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