Lie algebraic methods in integrable systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2000
|
| Schriftenreihe: | Chapman & Hall CRC research notes in mathematics series
415 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 354 S. |
| ISBN: | 1584880376 |
Internformat
MARC
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| 245 | 1 | 0 | |a Lie algebraic methods in integrable systems |c A. Roy Chowdhury |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2000 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
1 Introduction 1
1.1 Lax Equation and 1ST 3
1.2 Conserved Densities and Hamiltonian Structure 7
1.3 Symmetry Aspects 10
1.4 Observations 11
2 Lie Algebra 13
2.1 Introduction 13
2.2 Structure Constants and Basis of Lie Algebra 15
2.2.1 Special Linear Lie Algebra 16
2.3 Lie Groups and Lie Algebra 18
2.4 Representation of a Lie Algebra 20
2.5 Cartan Killing Form 24
2.6 Root Space Decomposition 26
2.7 Lie Groups: Finite and Infinite Dimensional 30
2.8 Loop Groups 32
2.9 The Virasoro Group 37
2.10 Quantum Tori Algebra 42
2.11 Kac Moody Algebra 48
2.12 Serre s Approach to Kac Moody Algebra 51
2.13 Gradation 54
2.14 Other Infinite Dimensional Lie Algebras 57
3 Prolongation Theory 75
3.1 Introduction 75
3.2 Sectioning of Forms 77
3.3 The KdV Problem 80
3.4 The Method of the Hall Structure 84
3.5 Prolongation in (2+1) Dimension 89
3.6 Method of Pseudopotentials 97
3.7 Prolongation Structure and the
Backlund Transformation 104
3.8 Constant Coefficient Ideal 109
3.9 Connections 111
3.10 Morphisms and Prolongation 114
3.11 Principal Prolongation Structure 119
3.12 Prolongations and Isovectors 127
3.13 Vessiot s Approach 132
3.14 Observations 136
4 Co adjoint Orbits 139
4.1 Introduction 139
4.2 The Kac Moody Algebra 141
4.3 Integrability Theorem: Adler, Kostant, Symes 144
4.4 Superingegrable Systems 149
4.5 Non Linear Partial Differential Equation 153
4.6 Extended AKS Theorem 161
4.7 Space Dependent Integrable Equation 164
4.8 The Moment Map 168
4.9 Moment Map in Relation to Integrable
Non Linear Equation 175
4.10 Co Adjoint Orbit of the Volterra Group 187
5 Symmetries of Integrable Systems 193
5.1 Introduction 193
5.2 Lie Point and Lie Backlund Symmetry 193
5.3 Lie Backlund Transformation 197
5.4 Some New Ideas in Symmetry Analysis 201
5.4.1 Gauge Transformation (Polyakov Approach) 202
5.4.2 Algebra of Lax Operator 210
5.4.3 Method of Fourier Analysis and Small
Amplitude Expansion 215
5.4.4 Hidden Symmetries 224
5.4.5 Approximate Symmetries 230
5.4.6 Kac Moody Symmetry 240
5.5 Non Local Symmetries 246
5.6 Observations 252
6 Hamiltonian Structure 255
6.1 Introduction 255
6.2 Drinfeld Sokolov Approach 255
6.3 The Lie Algebraic Approach 261
6.4 Example of Hamiltonian Structure and Reduction 265
6.5 Hamiltonian Reduction in (2+1) Dimension 268
6.6 Hamiltonian Reduction of Drinfeld and Sokolov 275
6.7 Krupershmidt s Approach 281
6.8 Gelfand Dikii Formula 289
6.9 Trace Identity and Hamiltonian Structure 294
6.10 Symmetry and Hamiltonian Structure 306
7 Classical r matrix 311
7.1 Introduction 311
7.2 Double Lie Algebra 313
7.3 Classical r matrix 319
7.4 The Use of r matrix 324
7.5 The r matrix and KP Equation 334
Index 347
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| id | DE-604.BV012543199 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:29:26Z |
| institution | BVB |
| isbn | 1584880376 |
| language | English |
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| physical | 354 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Chapman & Hall/CRC |
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| series | Chapman & Hall CRC research notes in mathematics series |
| series2 | Chapman & Hall CRC research notes in mathematics series |
| spelling | Roy Chowdhury, Asesh Verfasser (DE-588)122367685 aut Lie algebraic methods in integrable systems A. Roy Chowdhury Boca Raton [u.a.] Chapman & Hall/CRC 2000 354 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC research notes in mathematics series 415 Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s DE-604 Integrables System (DE-588)4114032-1 s Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 s Chapman & Hall CRC research notes in mathematics series 415 (DE-604)BV012456897 415 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008518302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roy Chowdhury, Asesh Lie algebraic methods in integrable systems Chapman & Hall CRC research notes in mathematics series Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd Integrables System (DE-588)4114032-1 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4229541-5 (DE-588)4114032-1 (DE-588)4130355-6 |
| title | Lie algebraic methods in integrable systems |
| title_auth | Lie algebraic methods in integrable systems |
| title_exact_search | Lie algebraic methods in integrable systems |
| title_full | Lie algebraic methods in integrable systems A. Roy Chowdhury |
| title_fullStr | Lie algebraic methods in integrable systems A. Roy Chowdhury |
| title_full_unstemmed | Lie algebraic methods in integrable systems A. Roy Chowdhury |
| title_short | Lie algebraic methods in integrable systems |
| title_sort | lie algebraic methods in integrable systems |
| topic | Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd Integrables System (DE-588)4114032-1 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Nichtlineares Differentialgleichungssystem Integrables System Lie-Algebra |
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