Basic methods of soliton theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1996
|
| Series: | Advanced series in mathematical physics
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | XI, 250 S. |
| ISBN: | 9810226438 |
Staff View
MARC
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| 300 | |a XI, 250 S. | ||
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| 650 | 7 | |a Solitons |2 ram | |
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| 650 | 4 | |a Mathematik | |
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Record in the Search Index
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| adam_text | ADVANCED SERIES IN MATHEMATICAL PHYSICS VOL. 25 BASIC METHODS OF SOLITON
THEORY IVAN CHEREDNIK UNIVERSITY OF NORTH CAROLINA, USA WORLD SCIENTIFIC
SINGAPORE »NEW JERSEY *LONDON HONG KONG CONTENTS PREFACE IX INTRODUCTION
1 AN OUTLINE OF THE MAIN DIRECTIONS 2 04. PLAN OF THIS BOOK 3 ISSUES
THAT HAVE BEEN LEFT OUT 4 0.2. CHIRAL FIELDS AND SIN-GORDON EQUATION 6
CHIRAL FIELDS ON SPHERES (A-MODEL) 8 FROM S 2 -FIELDS TO SIN-GORDON
EQUATION 9 0.3. GENERALIZED HEISENBERG MAGNET AND VNS EQUATION 10
REDUCTION TO VECTOR NONLINEAR SCHRODINGER EQUATION * 12 0.4. FOUR KEY
CONSTRUCTIONS 14 0.5. BASIC NOTATIONS 16 L CONSERVATION LAWS &
ALGEBRAIC-GEOMETRIC SOLUTIONS 18 91. LOCAL CONSERVATION LAWS 20 1.1.
FORMAL JOST FUNCTIONS 20 1.2. BASIC CONSTRUCTIONS 23 1.3. FORMAL JETS 27
1.4. DIRECT CALCULATIONS (RICCATI EQUATION) 30 RICCATI EQUATION 32 1.5.
LOCAL LAWS MODULO EXACT DERIVATIVES 34 POHLMEYER S LAW FOR PCF 34
Y- -FIELDS 36 1.6. COMMENTS 37 §2. GENERALIZED LAX EQUATIONS 38 2.1.
EQUATIONS OF THE GHM AND THE VNS TYPE 38 EQUATIONS OF THE VNS TYPE 41
2.2. JOST FUNCTIONS AS OPERATORS 42 2.3. ABSTRACT FRACTIONAL POWERS
(GENERATING OPERATOR) 45 GENERATING OPERATOR 48 2.4. GENERALIZED LAX
EQUATIONS (RELATIONS TO VNS) 50 FIRST ORDER OPERATOR 53 GENERATING
OPERATOR FOR LAX EQUATIONS 54 2.5. SCALAR OPERATORS (T-FUNCTIONS) 54
APPLICATIONS TO T-FUNCTIONS 56 LOCAL CONSERVATION LAWS 56 REDUCTION TO
THE MATRIX OPERATOR OF FIRST ORDER 57 HIGHER KDV EQUATIONS AND
SIN-GORDON 59 2.6. COMMENTS 60 §3. ALGEBRAIC-GEOMETRIC SOLUTIONS OF
BASIC EQUATIONS 62 3.1. BAKER FUNCTIONS 62 COMPUTATIONS OF BAKER
FUNCTIONS VIA THETA FUNCTIONS 64 3.2. THE MAIN CONSTRUCTION 67 JORDAN
FORM OF U, V 69 3.3. REALITY CONDITIONS 72 ANTI-HERMITICITY 11 3.4.
CURVES WITH AN INVOLUTION 79 - FLELDS 82 82 3.5. APPLICATION: DISCRETE
PCF EQUATION 83 3.6. COMMENTS 87 §4. ALGEBRAIC-GEOMETRIC SOLUTIONS OF
SIN-GORDON, NS, ETC. 89 4.1. SIN-GORDON EQUATION, S 2 -FIELDS 89
SOLUTIONS OF THE SIN-GORDON EQUATION 92 LIFTING A TO S 2 -FIELDS 94 4.2.
VNS EQUATION 97 CASE N = 2 (NS) 99 4.3. RELATIONS WITH THE CONSTRUCTIONS
IN §3 103 4.4. APPLICATION: THE DUALITY EQUATION 108 4.5. COMMENTS 111
N. BACKLUND TRANSFORMS AND INVERSE PROBLEM 113 §1. BACKLUND
TRANSFORMATIONS 115 1.1. TRANSFORMATIONS OF BASIC EQUATIONS 115 1.2.
BACKLUND TRANSFORMATIONS OF U M O N , AND S -FIELDS 120 O N -FIELDS
122 S N -FIELDS 123 1.3. SIN-GORDON EQUATION 128 RELATION WITH THE LAX
FORMALISM 130 1.4. APPLICATION: LOCAL CONSERVATION LAWS FOR THE
SIN-GORDON EQUATION AND S 1 -FIELDS 133 S^ -FIELDS 135 1.5. DARBOUX
TRANSFORMATION; NONLINEAR SCHRODINGER EQUATION 138 KDV EQUATION 140 NS
EQUATION 14 3 1.6. COMMENTS 145 82. INTRODUCTION TO THE SCATTERING
THEORY 148 2.1. MONODROMY MATRIX 148 2.2. ANALYTIC CONTINUATIONS 155
2.3. VARIANTS 164 UNITARITY CONDITIONS 167 THE CASE OF AN ARBITRARY
MATRIX UO 168 2.4. RIEMANN-HILBERT PROBLEM 171 2.5. VARIATIONAL
DERIVATIVES OF ENTRIES OF T (POISSON BRACKETS) 179 POISSON BRACKET 184
2.6. COMMENTS 187 3. APPLICATIONS OF THE INVERSE PROBLEM METHOD 190 3.1.
INVERSE PROBLEM FOR THE BASIC EQUATIONS 190 SCATTERING DATA 193 INVERSE
PROBLEM 197 3.2. ASYMPTOTIC EXPANSIONS AND TRACE FORMULAE 200
TRACEFORMULAE 204 3.3. EXAMPLES OF REDUCTION (O N , S ~ L -FIELDS; N =
2) 208 S^ -FIELDS 211 CASE N = 2 214 3.4. SCATTERING DATA FOR CERTAIN
SOLUTIONS OF THE NS EQUATION 217 SUPERPOSITION OF SEMI-SOLITIONS 222
VARIATIONS OF DISCRETE SPECTRAL DATA (N= ) 224 3.5. APPLICATION: DNS
EQUATION 226 N-SOLITON SOLUTIONS 230 COMPUTATION OF 8A FOR ONE-SOLITON
233 TRACEFORMULAE 235 3.6. COMMENTS 237 REFERENCES 239 INDEX 249
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:07Z |
| institution | BVB |
| isbn | 9810226438 |
| language | English |
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| oclc_num | 34150369 |
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| owner | DE-384 DE-188 |
| owner_facet | DE-384 DE-188 |
| physical | XI, 250 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series in mathematical physics |
| series2 | Advanced series in mathematical physics |
| spelling | Čerednik, Ivan Verfasser aut Basic methods of soliton theory Ivan Cherednik Singapore [u.a.] World Scientific 1996 XI, 250 S. txt rdacontent n rdamedia nc rdacarrier Advanced series in mathematical physics 25 Aus d. Russ. übers. Physique mathématique ram Solitons ram Équations différentielles ram Mathematik Differential equations, Nonlinear Numerical solutions Geometry, Algebraic Solitons Mathematics Soliton (DE-588)4135213-0 gnd rswk-swf Soliton (DE-588)4135213-0 s DE-604 Advanced series in mathematical physics 25 (DE-604)BV000900258 25 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009306245&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čerednik, Ivan Basic methods of soliton theory Advanced series in mathematical physics Physique mathématique ram Solitons ram Équations différentielles ram Mathematik Differential equations, Nonlinear Numerical solutions Geometry, Algebraic Solitons Mathematics Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4135213-0 |
| title | Basic methods of soliton theory |
| title_auth | Basic methods of soliton theory |
| title_exact_search | Basic methods of soliton theory |
| title_full | Basic methods of soliton theory Ivan Cherednik |
| title_fullStr | Basic methods of soliton theory Ivan Cherednik |
| title_full_unstemmed | Basic methods of soliton theory Ivan Cherednik |
| title_short | Basic methods of soliton theory |
| title_sort | basic methods of soliton theory |
| topic | Physique mathématique ram Solitons ram Équations différentielles ram Mathematik Differential equations, Nonlinear Numerical solutions Geometry, Algebraic Solitons Mathematics Soliton (DE-588)4135213-0 gnd |
| topic_facet | Physique mathématique Solitons Équations différentielles Mathematik Differential equations, Nonlinear Numerical solutions Geometry, Algebraic Solitons Mathematics Soliton |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009306245&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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