Continuous symmetries, Lie algebras and differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Mannheim ; Leizig ; Wien ; Zürich
BI-Wiss.-Verl.
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 297 - 307 |
| Beschreibung: | 320 S. graph. Darst. |
| ISBN: | 3411153911 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1817318914960392192 |
|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION 1
2 GROUPS 5
3 LIE GROUPS AND LIE TRANSFORMATION GROUPS 13
3.1 LIE GROUPS 13
3.2 LIE TRANSFORMATION GROUPS 14
3.2.1 CLASSICAL GROUPS 15
3.2.2 AFFINE GROUPS 24
3.2.3 GROUP ACTIONS (REALIZATIONS) AND GROUP REPRESENTATIONS 27
3.3 GENERAL REMARKS ON LIE GROUPS 33
4 INFINITESIMAL TRANSFORMATIONS AND GENERATORS 39
4.1 INFINITESIMAL TRANSFORMATIONS 39
4.2 INFINITESIMAL GENERATORS 43
4.3 MULTI-PARAMETER TRANSFORMATION GROUPS 47
5 LIE ALGEBRAS 53
5.1 DEFINITION AND EXAMPLES OF LIE ALGEBRAS 53
5.2 LOCAL LIE GROUP REPRESENTATION 55
5.3 CLASSICAL LIE ALGEBRAS 60
5.4 IMPORTANT CONCEPTS AND EXAMPLES 64
6 INTRODUCTORY EXAMPLES 73
6.1 THE ONE-DIMENSIONAL LINEAR WAVE EQUATION 73
6.2 THE LINEAR ONE-DIMENSIONAL DIFFUSION EQUATION 77
6.3 STATIONARY FLOW 78
6.4 GAUGE TRANSFORMATION 81
7 THE LIE DERIVATIVE AND INVARIANCE 89
7.1 DIFFERENTIAL FORMS 89
7.2 THE LIE DERIVATIVE 104
7.3 INVARIANCE AND CONFORMAL INVARIANCE 107
HTTP://D-NB.INFO/920169112
8 PROLONGATION AND INVARIANCE 117
8.1 JET BUNDLE FORMALISM 117
8.1.1 INTRODUCTORY EXAMPLE 117
8.1.2 LOCAL JET BUNDLE FORMALISM 119
8.1.3 PROLONGATION OF THE VECTOR FIELD 124
8.1.4 PARTIAL DIFFERENTIAL EQUATIONS ON JET BUNDLES 126
8.2 INVARIANCE OF DIFFERENTIAL EQUATIONS 128
8.3 SIMILARITY SOLUTIONS 133
9 LIE-BACKLUND VECTOR FIELDS 143
9.1 BACKLUND VECTOR FIELDS 143
9.2 INVARIANT SOLUTIONS 152
10 DIFFERENTIAL EQUATION FOR A GIVEN LIE ALGEBRA 155
10.1 LIE POINT SYMMETRY VECTOR FIELDS 155
10.2 LIE-BACKLUND VECTOR FIELDS 160
11 A LIST O
F
LIE SYMMETRY VECTOR FIELDS 163
12 RECURSION OPERATORS 187
12.1 GATEAUX DERIVATIVE AND RECURSION OPERATORS 187
12.2 BACKLUND TRANSFORMATIONS 199
12.3 THE LAX REPRESENTATION 206
13 CONSERVATION LAWS 213
13.1 BASIC CONCEPTS 213
13.2 EXTERIOR DIFFERENTIAL SYSTEMS AND CARTAN'S FORM 219
14 SYMMETRIES AND PAINLEVE TEST 237
14.1 ORDINARY DIFFERENTIAL EQUATIONS 237
14.1.1 POINT TRANSFORMATION AND PAINLEVE TEST 243
14.2 PARTIAL DIFFERENTIAL EQUATIONS 247
14.3 SYMMETRIES BY TRUNCATED EXPANSIONS 250
14.4 PAINLEVE TEST AND RECURSION OPERATORS 253
14.5 SINGULAR MANIFOLD 255
15 LIE ALGEBRA VALUED DIFFERENTIAL FORMS 261
16 BOSE OPERATORS AND LIE ALGEBRAS 275
17 COMPUTER ALGEBRA 283
17.1 COMPUTER ALGEBRA PACKAGES 283
17.2 PROGRAMS FOR CALCULATING VECTOR FIELDS 285
A DIFFERENTIATE MANIFOLDS 289 |
| any_adam_object | 1 |
| author | Euler, Norbert Steeb, Willi-Hans 1945- |
| author_GND | (DE-588)12155614X |
| author_facet | Euler, Norbert Steeb, Willi-Hans 1945- |
| author_role | aut aut |
| author_sort | Euler, Norbert |
| author_variant | n e ne w h s whs |
| building | Verbundindex |
| bvnumber | BV025859386 |
| classification_rvk | SK 340 SK 500 |
| ctrlnum | (OCoLC)243715320 (DE-599)BVBBV025859386 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025859386 |
| illustrated | Illustrated |
| indexdate | 2024-12-02T09:06:12Z |
| institution | BVB |
| isbn | 3411153911 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019107130 |
| oclc_num | 243715320 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | 320 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | BI-Wiss.-Verl. |
| record_format | marc |
| spelling | Euler, Norbert Verfasser aut Continuous symmetries, Lie algebras and differential equations by Norbert Euler and Willi-Hans Steeb Mannheim ; Leizig ; Wien ; Zürich BI-Wiss.-Verl. 1992 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 297 - 307 Kontinuierliche Gruppe (DE-588)4165160-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Kontinuierliche Gruppe (DE-588)4165160-1 s Lie-Algebra (DE-588)4130355-6 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Steeb, Willi-Hans 1945- Verfasser (DE-588)12155614X aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019107130&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Euler, Norbert Steeb, Willi-Hans 1945- Continuous symmetries, Lie algebras and differential equations Kontinuierliche Gruppe (DE-588)4165160-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4165160-1 (DE-588)4044779-0 (DE-588)4012249-9 (DE-588)4130355-6 |
| title | Continuous symmetries, Lie algebras and differential equations |
| title_auth | Continuous symmetries, Lie algebras and differential equations |
| title_exact_search | Continuous symmetries, Lie algebras and differential equations |
| title_full | Continuous symmetries, Lie algebras and differential equations by Norbert Euler and Willi-Hans Steeb |
| title_fullStr | Continuous symmetries, Lie algebras and differential equations by Norbert Euler and Willi-Hans Steeb |
| title_full_unstemmed | Continuous symmetries, Lie algebras and differential equations by Norbert Euler and Willi-Hans Steeb |
| title_short | Continuous symmetries, Lie algebras and differential equations |
| title_sort | continuous symmetries lie algebras and differential equations |
| topic | Kontinuierliche Gruppe (DE-588)4165160-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Kontinuierliche Gruppe Partielle Differentialgleichung Differentialgleichung Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019107130&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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