Integrability:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Lecture Notes in Physics
767 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 339 S. |
| ISBN: | 9783540881100 9783540881117 |
Internformat
MARC
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| 245 | 1 | 0 | |a Integrability |c A. V. Mikhailov (ed.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 339 S. | ||
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Datensatz im Suchindex
| _version_ | 1804138480600612864 |
|---|---|
| adam_text | CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A.V. MIKHAILOV
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 15 1 SYMMETRIES OF
DIFFERENTIAL EQUATIONS AND THE PROBLEM OF INTEGRABILITY 19 A.V.
MIKHAILOV AND V.V. SOKOLOV 1.1 INTRODUCTION . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2
SYMMETRIES AND FIRST INTEGRALS OF FINITE-DIMENSIONAL DYNAMICAL SYSTEMS .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 20 1.3 BASIC CONCEPTS OF THE SYMMETRY APPROACH .
. . . . . . . . . . . . . . . . . . 32 1.4 MODIFICATIONS AND
GENERALIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.5 SHORT DESCRIPTION OF SOLVED CLASSIFICATION PROBLEMS AND REFERENCES .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 73 REFERENCES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2 NUMBER
THEORY AND THE SYMMETRY CLASSIFICATION OF INTEGRABLE SYSTEMS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 89 J.A. SANDERS AND J.P. WANG 2.1 INTRODUCTION .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 89 2.2 THE SYMBOLIC METHOD . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 91 2.3 AN IMPLICIT
FUNCTION THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 96 2.4 SYMMETRY-INTEGRABLE EVOLUTION EQUATIONS . . . . . . . . . . .
. . . . . . . . . 98 2.5 EVOLUTION SYSTEMS WITH K COMPONENTS . . . . . .
. . . . . . . . . . . . . . . . . 105 2.6 ONE SYMMETRY DOES NOT IMPLY
INTEGRABILITY . . . . . . . . . . . . . . . . . . . 108 2.7 CONCLUDING
REMARKS, OPEN PROBLEMS AND FURTHER DEVELOPMENT . . 113 2.8 SOME
IRREDUCIBILITY RESULTS BY F. BEUKERS . . . . . . . . . . . . . . . . . .
. . . 114 2.9 THE FILTERED LIE ALGEBRA VERSION OF THE IMPLICIT FUNCTION
THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 115 REFERENCES . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 116 3 FOUR LECTURES: DISCRETIZATION AND INTEGRABILITY.
DISCRETE SPECTRAL SYMMETRIES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 S.P. NOVIKOV
3.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 119 XI XII CONTENTS 3.2 CONTINUOUS
AND DISCRETE SPECTRAL SYMMETRIES OF 1D SYSTEMS AND SPECTRAL THEORY OF
OPERATORS. 1D CONTINUOUS SCHR¨ ODINGER OPERATOR AND ITS DISCRETE
ANALOGUE . . . . . . . . . . . . . . . . . . . . . . . . . . 120 3.3 2D
SCHR¨ ODINGER OPERATOR. DISCRETE SPECTRAL SYMMETRIES, SPECTRAL THEORY OF
THE SELECTED ENERGY LEVEL AND SPACE/LATTICE DISCRETIZATION . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 124 3.4 DISCRETIZATION OF THE 2D SCHR¨ ODINGER OPERATORS AND LAPLACE
TRANSFORMATIONS ON THE SQUARE AND EQUILATERAL LATTICES . . . . . . . . .
128 3.5 2D MANIFOLDS WITH THE COLORED BLACK*WHITE TRIANGULATION.
INTEGRABLE SYSTEMS ON A TRIVALENT TREE. . . . . . . . . . . . . . . . .
. . . . . . . 133 REFERENCES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4
SYMMETRIES OF SPECTRAL PROBLEMS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 139 A. SHABAT 4.1 LIE-TYPE SYMMETRIES . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.2 DISCRETE SYMMETRIES. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 153 REFERENCES . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 172 5 NORMAL FORM AND SOLITONS . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 175 Y. HIRAOKA AND Y. KODAMA 5.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 175 5.2 PERTURBED KDV EQUATION . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.3
CONSERVED QUANTITIES AND N -SOLITON SOLUTIONS . . . . . . . . . . . . .
. . . . 180 5.4 SYMMETRY AND THE PERTURBED EQUATION . . . . . . . . . .
. . . . . . . . . . . . . . 184 5.5 NORMAL FORM THEORY . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.6
INTERACTIONS OF SOLITARY WAVES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 195 5.7 EXAMPLES . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 212 6 MULTISCALE EXPANSION
AND INTEGRABILITY OF DISPERSIVE WAVE EQUATIONS . 215 A. DEGASPERIS 6.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 215 6.2 NONLINEAR SCHR¨ ODINGER-TYPE
MODEL EQUATIONS AND INTEGRABILITY . . 225 6.3 HIGHER ORDER TERMS AND
INTEGRABILITY . . . . . . . . . . . . . . . . . . . . . . . . . 234
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 243 7 PAINLEV´ E TESTS,
SINGULARITY STRUCTURE AND INTEGRABILITY . . . . . . . . . . . . . . 245
A.N.W. HONE 7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 245 7.2 PAINLEV´ E
ANALYSIS FOR ODES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 249 7.3 THE ABLOWITZ*RAMANI*SEGUR CONJECTURE . . . . . . . . .
. . . . . . . . . . . . 254 7.4 THE WEISS*TABOR*CARNEVALE PAINLEV´ E
TEST . . . . . . . . . . . . . . . . . . . . 257 7.5 TRUNCATION
TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 261 7.6 WEAK PAINLEV´ E TESTS . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 267 7.7 OUTLOOK . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 273 REFERENCES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
CONTENTS XIII 8 HIROTA*S BILINEAR METHOD AND ITS CONNECTION WITH
INTEGRABILITY . . . . . . . 279 J. HIETARINTA 8.1 WHY THE BILINEAR FORM?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
279 8.2 FROM NONLINEAR TO BILINEAR (KDV) . . . . . . . . . . . . . . . .
. . . . . . . . . . . 280 8.3 MULTISOLITON SOLUTIONS FOR THE KDV CLASS .
. . . . . . . . . . . . . . . . . . . . 283 8.4 SOLITON SOLUTION FOR THE
MKDV AND SG CLASS . . . . . . . . . . . . . . . . . . 290 8.5 THE
NONLINEAR SCHR¨ ODINGER EQUATION . . . . . . . . . . . . . . . . . . . .
. . . . . 294 8.6 HIERARCHIES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 303 8.7 BILINEAR B¨
ACKLUND TRANSFORMATION . . . . . . . . . . . . . . . . . . . . . . . . .
. . 305 8.8 THE THREE-SOLITON CONDITION AS AN INTEGRABILITY TEST . . . .
. . . . . . . . 306 8.9 FROM BILINEAR TO NONLINEAR . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 310 8.10 CONCLUSIONS . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 312 REFERENCES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 9
INTEGRABILITY OF THE QUANTUM XXZ HAMILTONIAN . . . . . . . . . . . . . .
. . . . . . 315 T. MIWA 9.1 INTEGRABILITY . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 9.2
SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 319 REFERENCES . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 323 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
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| id | DE-604.BV035218575 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:28:52Z |
| institution | BVB |
| isbn | 9783540881100 9783540881117 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017024684 |
| oclc_num | 297583279 |
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| owner | DE-384 DE-703 DE-11 |
| owner_facet | DE-384 DE-703 DE-11 |
| physical | XIII, 339 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Physics |
| series2 | Lecture Notes in Physics |
| spelling | Integrability A. V. Mikhailov (ed.) Berlin [u.a.] Springer 2009 XIII, 339 S. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Physics 767 Integrables System (DE-588)4114032-1 gnd rswk-swf Integrierbarkeit (DE-588)4474751-2 gnd rswk-swf Integrables System (DE-588)4114032-1 s DE-604 Integrierbarkeit (DE-588)4474751-2 s Mikhailov, Alexander 1953- Sonstige (DE-588)136866492 oth Lecture Notes in Physics 767 (DE-604)BV000003166 767 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017024684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Integrability Lecture Notes in Physics Integrables System (DE-588)4114032-1 gnd Integrierbarkeit (DE-588)4474751-2 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4474751-2 |
| title | Integrability |
| title_auth | Integrability |
| title_exact_search | Integrability |
| title_full | Integrability A. V. Mikhailov (ed.) |
| title_fullStr | Integrability A. V. Mikhailov (ed.) |
| title_full_unstemmed | Integrability A. V. Mikhailov (ed.) |
| title_short | Integrability |
| title_sort | integrability |
| topic | Integrables System (DE-588)4114032-1 gnd Integrierbarkeit (DE-588)4474751-2 gnd |
| topic_facet | Integrables System Integrierbarkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017024684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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