Soliton equations and Hamiltonian systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2003
|
| Edition: | 2. ed. |
| Series: | Advanced series in mathematical physics
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 408 S. |
| ISBN: | 9812381732 |
Staff View
MARC
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| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2003 | |
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Record in the Search Index
| _version_ | 1804129483188338688 |
|---|---|
| adam_text | ADVANCED SERIES IN SOLITON EQUATIONS AND HAMILTONIAN SYSTEMS SECOND
EDITION LA. DICKEY DEPARTMENT OF MATHEMATICS UNIVERSITY OF OKLAHOMA, USA
WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * HONG KONG CONTENTS
INTRODUCTION TO THE FIRST EDITION 1 CHAPTER 1 INTEGRABLE SYSTEMS
GENERATED BY LINEAR DIFFERENTIAL NTH ORDER OPERATORS 7 1.1 DIFFERENTIAL
ALGEBRA A 7 1.2 SPACE OF FUNCTIONAL A 8 1.3 RING OF PSEUDODIFFERENTIAL
OPERATORS 9 1.4 LAX PAIRS. GD HIERARCHIES OF EQUATIONS 12 1.5 FIRST
INTEGRALS (CONSTANTS OF MOTION) 14 1.6 COMPATIBILITY OF THE EQUATIONS OF
A HIERARCHY 15 1.7 SOLITON SOLUTIONS 16 1.8 RESOLVENT. ADLER MAPPING 18
CHAPTER 2 HAMILTONIAN STRUCTURES 23 2.1 FINITE-DIMENSIONAL CASE 23 2.2
HAMILTON MAPPING 28 2.3 VARIATIONAL PRINCIPLES 29 2.4 SYMPLECTIC FORM
ON AN ORBIT OF THE COADJOINT REPRESENTATION OF A LIE GROUP 33 2.5 PURELY
ALGEBRAIC TREATMENT OF THE HAMILTONIAN STRUCTURE 36 2.6 EXAMPLES ....-.
39 CHAPTER 3 HAMILTONIAN STRUCTURE OF THE GD HIERARCHIES 45 3.1 LIE
ALGEBRA V, DUAL SPACED 1 , AND MODULE N 45 3.2 PROOF OF THEOREM 3.1.2
48 3.3 POISSON BRACKET 53 VIII CONTENTS 3.4 REDUCTION TO THE SUBMANIFOLD
W N -I =0 56 3.5 VARIATIONAL DERIVATIVE OF THE RESOLVENT 57 3.6
HAMILTONIANS OF THE GD HIERARCHIES . . 59 3.7 THEORY OF THE
KDV-HIERARCHY (N = 2) INDEPENDENT OF THE GENERAL CASE 60 CHAPTER 4
MODIFIED KDV AND GD. THE KUPERSHMIDT*WILSON THEOREM 67 4.1 MIURA
TRANSFORMATION. THE KUPERSHMIDT-WILSON THEOREM 67 4.2 MODIFIED KDV
EQUATION. BACKLUND TRANSFORMATIONS 71 4.3 MORE ON MODIFIED GD EQUATIONS
72 CHAPTER 5 THE KP HIERARCHY 75 5.1 DEFINITION OF THE KP HIERARCHY 75
5.2 REDUCTION OF THE KP HIERARCHY TO GD 77 5.3 FIRST INTEGRALS AND
SOLITON SOLUTIONS 79 5.4 HAMILTONIAN STRUCTURE 81 5.5 RESOLVENT 84 5.6
HAMILTONIANS OF THE KP HIERARCHY 87 CHAPTER 6 BAKER FUNCTION, R-FUNCTION
89 6.1 DRESSING 89 6.2 BAKER FUNCTION 90 6.3 SHIFT OPERATOR AND
T-FUNCTION 94 6.4 RESOLVENT AND BAKER FUNCTION. FAY IDENTITIES 100 6.5
VERTEX OPERATORS 103 6.6 T-FUNCTION AND FOCK REPRESENTATION 106 6A
APPENDIX. LIST OF USEFUL FORMULAS FOR THE FAA DI BRUNO POLYNOMIALS ILL
CHAPTER 7 ADDITIONAL SYMMETRIES, STRING EQUATION 113 7.1 ADDITIONAL
SYMMETRIES 113 7.2 GENERATING FUNCTION FOR ADDITIONAL SYMMETRIES 117 7.3
STRING EQUATION 119 CHAPTER 8 GRASSMANNIAN. ALGEBRAIC-GEOMETRICAL
KRICHEVER SOLUTIONS 123 8.1 INFINITE-DIMENSIONAL GRASSMANNIAN 123 8.2
MODIFIED DEFINITION OF THE GRASSMANNIAN T-FUNCTION 128 CONTENTS IX 8.3
ALGEBRAIC-GEOMETRICAL SOLUTIONS OF KRICHEVER 132 8A APPENDIX. ABEL
MAPPING AND THE ^-FUNCTION 137 CHAPTER 9 MATRIX FIRST-ORDER OPERATOR,
AKNS-D HIERARCHY 141 9.1 HIERARCHY OF EQUATIONS GENERATED BY A
FIRST-ORDER MATRIX DIFFERENTIAL OPERATOR 141 9.2 HAMILTONIAN STRUCTURE .
. . 147 9.3 HAMILTONIANS OF THE AKNS-D HIERARCHY 151 9.4 GD HIERARCHIES
AS REDUCTIONS OF THE MATRIX HIERARCHIES (DRINFELD-SOKOLOV REDUCTION) 154
9A APPENDIX. EXTENSION OF THE ALGEBRA A TO AN ALGEBRA CLOSED WITH
RESPECT TO THE INDEFINITE INTEGRATION 162 CHAPTER 10 GENERALIZATION OF
THE AKNS-D HIERARCHY: SINGLE-POLE AND MULTI-POLE MATRIX HIERARCHIES 165
10.1 SINGLE-POLE MATRIX HIERARCHY ~. 165 10.2 SINGLE-POLE HIERARCHY.
PRESENTATION NOT DEPENDING ON A DISTINGUISHED OPERATOR 1 171 10.3
MULTI-POLE (GENERAL ZAKHAROV-SHABAT) HIERARCHY 173 10.4 EXAMPLE:
PRINCIPAL CHIRAL FIELD EQUATION 177 10.5 GRASSMANNIAN , 178 CHAPTER 11
ISOMONODROMIC DEFORMATIONS AND THE MOST GENERAL MATRIX HIERARCHY 187
11.1 ISOMONODROMIC DEFORMATIONS . 187 11.2 GENERAL MATRIX HIERARCHY 195
CHAPTER 12 TAU FUNCTIONS OF MATRIX HIERARCHIES 203 12.1 SEGAL-WILSON S
T-FUNCTION FOR AKNS-D 203 12.2 TAU FUNCTIONS FOR MORE GENERAL MATRIX
HIERARCHIES 209 CHAPTER 13 KP, MODIFIED KP, CONSTRAINED KP, DISCRETE KP,
AND Q-KP 213 13.1 MODIFIED GD (CONT D) 213 13.2 MODIFIED KP AND
CONSTRAINED KP 215 13.3 DISCRETE KP 220 13.4 Q-KP 224 X CONTENTS CHAPTER
14 ANOTHER CHAIN OF KP HIERARCHIES AND INTEGRALS OVER MATRIX VARIETIES
227 14.1 INTRODUCTION. MORE ABOUT THE MODIFIED KP 227 14.2 STABILIZING
CHAIN .... . 231 14.3 SOLUTIONS TO THE CHAIN . . 234 14.4 SOLUTIONS IN
THE FORM OF SERIES IN SCHUR POLYNOMIALS. STABILIZATION 237 14.5 FROM THE
STABILIZING CHAIN TO THE KONTSEVICH INTEGRAL 239 CHAPTER 15
TRANSFORMATIONAL PROPERTIES OF A DIFFERENTIAL OPERATOR UNDER
DIFFEOMORPHISMS AND CLASSICAL W-ALGEBRAS 251 15.1 TENSORS WITH RESPECT
TO DIFFEOMORPHISMS AND THE . AGD-ALGEBRA 251 15.2 ANOTHER CONSTRUCTION
OF PRIMARY FIELDS 262 CHAPTER 16 FURTHER RESTRICTIONS OF THE KP;
STATIONARY EQUATIONS 269 16.1 THE RING OF FUNCTIONS ON THE PHASE SPACE
OF THE EQUATION 269 16.2 CHARACTERISTICS OF THE FIRST INTEGRALS 272 16.3
HAMILTONIAN STRUCTURE 273 16.4 STATIONARY EQUATIONS OF THE KDV HIERARCHY
([GD79]) 278 16.5 INTEGRATION AFTER LIOUVILLE 284 16.6 RETURN TO THE
ORIGINAL VARIABLES . . . 289 CHAPTER 17 STATIONARY EQUATIONS OF THE
MATRIX HIERARCHY 295 17.1 FIRST INTEGRALS 295 17.2 HAMILTONIAN STRUCTURE
OF STATIONARY EQUATIONS 303 17.3 ACTION-ANGLE VARIABLES^ 308 17A
APPENDIX. GENUS OF THE RIEMANN SURFACES AND THE NEWTON DIAGRAM . . 312
CHAPTER 18 STATIONARY EQUATIONS OF THE MATRIX HIERARCHY (CONT D) 317
18.1 BAKER FUNCTION. RETURN TO ORIGINAL VARIABLES 317 18.2 ROTATION OF
THE N-DIMENSIONAL RIGID BODY 323 CONTENTS XI CHAPTER 19 FIELD LAGRANGIAN
AND HAMILTONIAN FORMALISM 329 19.1 INTRODUCTION 329 19.2 VARIATIONAL
BI-COMPLEX 331 19.3 EXACTNESS OF THE BI-COMPLEX 336 19.4 VARIATIONAL
DERIVATIVE 342 19.5 LAGRANGIAN-HAMILTONIAN FORMALISM 346 19.6
VARIATIONAL BI-COMPLEX OF A DIFFERENTIAL EQUATION. FIRST INTEGRALS 350
19.7 POISSON BRACKET 356 19.8 RELATIONSHIP WITH THE SINGLE-TIME
FORMALISM 357 CHAPTER 20 FURTHER EXAMPLES AND APPLICATIONS 363 20.1
KP-HIERARCHY 363 20.2 THE ZAKHAROV-SHABAT EQUATION WITH RATIONAL
DEPENDENCE ON THE SPECTRAL PARAMETER 368 20.3 PRINCIPAL CHIRAL FIELD 384
20.4 LAGRANGIANS OF THE NTH REDUCED KP (GD) HIERARCHY 392 BIBLIOGRAPHY
397 INDEX 407
|
| any_adam_object | 1 |
| author | Dickey, Leonid A. |
| author_facet | Dickey, Leonid A. |
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| discipline | Physik Mathematik |
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| id | DE-604.BV014758126 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:05:51Z |
| institution | BVB |
| isbn | 9812381732 |
| language | English |
| lccn | 2002033186 |
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| physical | XI, 408 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series in mathematical physics |
| series2 | Advanced series in mathematical physics |
| spelling | Dickey, Leonid A. Verfasser aut Soliton equations and Hamiltonian systems L.A. Dickey 2. ed. New Jersey [u.a.] World Scientific 2003 XI, 408 S. txt rdacontent n rdamedia nc rdacarrier Advanced series in mathematical physics 26 Hamiltonian systems Solitons Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Soliton (DE-588)4135213-0 s Hamiltonsches System (DE-588)4139943-2 s Mathematische Physik (DE-588)4037952-8 s DE-604 Hamilton-Formalismus (DE-588)4376155-0 s 1\p DE-604 Advanced series in mathematical physics 26 (DE-604)BV000900258 26 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009994079&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dickey, Leonid A. Soliton equations and Hamiltonian systems Advanced series in mathematical physics Hamiltonian systems Solitons Hamiltonsches System (DE-588)4139943-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4037952-8 (DE-588)4376155-0 (DE-588)4135213-0 |
| title | Soliton equations and Hamiltonian systems |
| title_auth | Soliton equations and Hamiltonian systems |
| title_exact_search | Soliton equations and Hamiltonian systems |
| title_full | Soliton equations and Hamiltonian systems L.A. Dickey |
| title_fullStr | Soliton equations and Hamiltonian systems L.A. Dickey |
| title_full_unstemmed | Soliton equations and Hamiltonian systems L.A. Dickey |
| title_short | Soliton equations and Hamiltonian systems |
| title_sort | soliton equations and hamiltonian systems |
| topic | Hamiltonian systems Solitons Hamiltonsches System (DE-588)4139943-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Soliton (DE-588)4135213-0 gnd |
| topic_facet | Hamiltonian systems Solitons Hamiltonsches System Mathematische Physik Hamilton-Formalismus Soliton |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009994079&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000900258 |
| work_keys_str_mv | AT dickeyleonida solitonequationsandhamiltoniansystems |