Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
CWI
1988
|
| Schriftenreihe: | CWI Tracts
50 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 180 S. |
| ISBN: | 9061963516 |
Internformat
MARC
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| 100 | 1 | |a Kerf, Fred de |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems |c F. de Kerf |
| 264 | 1 | |a Amsterdam |b CWI |c 1988 | |
| 300 | |a 180 S. | ||
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| 490 | 1 | |a CWI Tracts |v 50 | |
| 650 | 7 | |a Analyse mathématique |2 ram | |
| 650 | 7 | |a Développements asymptotiques |2 ram | |
| 650 | 7 | |a Perturbation (Mathématiques) |2 ram | |
| 650 | 7 | |a Problèmes aux valeurs initiales |2 ram | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Initial value problems | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Perturbation (Mathematics) | |
| 650 | 0 | 7 | |a Korteweg-de-Vries-Gleichung |0 (DE-588)4287203-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Anfangswertproblem |0 (DE-588)4001991-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Korteweg-de-Vries-Gleichung |0 (DE-588)4287203-0 |D s |
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Datensatz im Suchindex
| _version_ | 1804135990349004800 |
|---|---|
| adam_text | CONTENTS
CHAPTER I INTRODUCTION 1
1. Historical introduction 1
2. Main goal of this research Short description of the way
by which this goal is achieved 2
3. Summary of the contents 5
CHAPTER II FUNDAMENTALS 8
1. The Inverse Scattering Transform 8
2. Scattering properties of the one dimensional, time independent
Schrodinger Equation 12
3. Inverse scattering for the Schrodinger Equation;
The 1ST applied to the KdV initial value problem 27
CHAPTER III EMERGENCE OF SOLITONS FOR THE pKdV 31
1. Evolution of the spectral data for potentials satisfying
the pKdV 31
2. Asymptotic behaviour of ei gen functions iji (x,t);
The emergence of solitons 36
CHAPTER IV APPROXIMATING A POTENTIAL IN THE SCHRODINGER EQUATION
BY ITS ASSOCIATED SOLITON POTENTIAL 53
1. Theorems based on the work of W. Eckhaus and P.C. Schuur 53
2. Theorems based on the Trace formula 67
CHAPTER V APPLYING THE THEOREMS OF CHAPTER IV TO SOLUTIONS OF
THE pKdV 82
1. Results on 6 (e) timescales with 5(e) *£p, 0 £ p 1 82
2. Consistency results on the —timescale 94
CHAPTER VI EXPLICIT APPROXIMATIONS FOR SOLUTIONS OF THE
pKdV INITIAL VALUE PROBLEM 107
CHAPTER VII EXAMPLES, APPLICATIONS AND EXTENSIONS 117
1. A trivial but illustrative example, f(u) « u 117
2. Pure polynomial perturbations 122
3. The shallow water wave perturbation,
f(u) = |u2u +5+23_19 124
2 x 2 xxx 4 x xx 40 xxxxx
4. The inadmissible perturbation f(u) = u + ixu 127
APPENDIX A 134
1. Derivation of (2.1.14) and (2.1.15);
Evolution of the spectral data for solutions of these equations;
The solitary wave solutions of (2.1.14) and (2.1.17) 134
2. i) Proof of Theorem (2.2.3) 140
ii) Proof of (2.2.36) 141
iii) Proof of Theorem (2.2.4) 142
iv) Proof of Theorem (2.2.6) 145
v) Proof of Lemma (2.2.1) 147
APPENDIX B 1*8
1. The evolution equations for y (t) and a(k,t) 148
2. Well definedness of 6 and H 152
n n
APPENDIX C Proof that (5.1.10) can be replaced by the conditions
(5.1.24) and (5.1.25) 158
APPENDIX D PROOFS OF LEMMAS (6.1) ANP (6.2) 160
i) Proof of Lemma (6.1) 160
ii) Proof of Lemma (6.2) 161
APPENDIX E 165
1. Derivation of the KdV equation for shallow water waves 165
2. Solving (7.4.6) 169
REFERENCES 172
LIST OF SYMBOLS 176
SUBJECT INDEX 178
|
| adam_txt |
CONTENTS
CHAPTER I INTRODUCTION 1
1. Historical introduction 1
2. Main goal of this research Short description of the way
by which this goal is achieved 2
3. Summary of the contents 5
CHAPTER II FUNDAMENTALS 8
1. The Inverse Scattering Transform 8
2. Scattering properties of the one dimensional, time independent
Schrodinger Equation 12
3. Inverse scattering for the Schrodinger Equation;
The 1ST applied to the KdV initial value problem 27
CHAPTER III EMERGENCE OF SOLITONS FOR THE pKdV 31
1. Evolution of the spectral data for potentials satisfying
the pKdV 31
2. Asymptotic behaviour of ei gen functions iji (x,t);
The emergence of solitons 36
CHAPTER IV APPROXIMATING A POTENTIAL IN THE SCHRODINGER EQUATION
BY ITS ASSOCIATED SOLITON POTENTIAL 53
1. Theorems based on the work of W. Eckhaus and P.C. Schuur 53
2. Theorems based on the Trace formula 67
CHAPTER V APPLYING THE THEOREMS OF CHAPTER IV TO SOLUTIONS OF
THE pKdV 82
1. Results on 6 (e) timescales with 5(e) *£p, 0 £ p 1 82
2. Consistency results on the —timescale 94
CHAPTER VI EXPLICIT APPROXIMATIONS FOR SOLUTIONS OF THE
pKdV INITIAL VALUE PROBLEM 107
CHAPTER VII EXAMPLES, APPLICATIONS AND EXTENSIONS 117
1. A trivial but illustrative example, f(u) « u 117
2. Pure polynomial perturbations 122
3. The shallow water wave perturbation,
f(u) = |u2u +5+23_19 124
2 x 2 xxx 4 x xx 40 xxxxx
4. The inadmissible perturbation f(u) = u + ixu 127
APPENDIX A 134
1. Derivation of (2.1.14) and (2.1.15);
Evolution of the spectral data for solutions of these equations;
The solitary wave solutions of (2.1.14) and (2.1.17) 134
2. i) Proof of Theorem (2.2.3) 140
ii) Proof of (2.2.36) 141
iii) Proof of Theorem (2.2.4) 142
iv) Proof of Theorem (2.2.6) 145
v) Proof of Lemma (2.2.1) 147
APPENDIX B 1*8
1. The evolution equations for y (t) and a(k,t) 148
2. Well definedness of 6 and H 152
n n
APPENDIX C Proof that (5.1.10) can be replaced by the conditions
(5.1.24) and (5.1.25) 158
APPENDIX D PROOFS OF LEMMAS (6.1) ANP (6.2) 160
i) Proof of Lemma (6.1) 160
ii) Proof of Lemma (6.2) 161
APPENDIX E 165
1. Derivation of the KdV equation for shallow water waves 165
2. Solving (7.4.6) 169
REFERENCES 172
LIST OF SYMBOLS 176
SUBJECT INDEX 178 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:12:06Z |
| indexdate | 2024-07-09T20:49:17Z |
| institution | BVB |
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| physical | 180 S. |
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| spelling | Kerf, Fred de Verfasser aut Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems F. de Kerf Amsterdam CWI 1988 180 S. txt rdacontent n rdamedia nc rdacarrier CWI Tracts 50 Analyse mathématique ram Développements asymptotiques ram Perturbation (Mathématiques) ram Problèmes aux valeurs initiales ram Asymptotic expansions Initial value problems Mathematical analysis Perturbation (Mathematics) Korteweg-de-Vries-Gleichung (DE-588)4287203-0 gnd rswk-swf Anfangswertproblem (DE-588)4001991-3 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Anfangswertproblem (DE-588)4001991-3 s DE-604 Korteweg-de-Vries-Gleichung (DE-588)4287203-0 s CWI Tracts 50 (DE-604)BV001902011 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015230854&sequence=000002&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 | Kerf, Fred de Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems CWI Tracts Analyse mathématique ram Développements asymptotiques ram Perturbation (Mathématiques) ram Problèmes aux valeurs initiales ram Asymptotic expansions Initial value problems Mathematical analysis Perturbation (Mathematics) Korteweg-de-Vries-Gleichung (DE-588)4287203-0 gnd Anfangswertproblem (DE-588)4001991-3 gnd |
| subject_GND | (DE-588)4287203-0 (DE-588)4001991-3 (DE-588)4113937-9 |
| title | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems |
| title_auth | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems |
| title_exact_search | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems |
| title_exact_search_txtP | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems |
| title_full | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems F. de Kerf |
| title_fullStr | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems F. de Kerf |
| title_full_unstemmed | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems F. de Kerf |
| title_short | Asymptotic analysis of a class of perturbed Korteweg- de Vries initial value problems |
| title_sort | asymptotic analysis of a class of perturbed korteweg de vries initial value problems |
| topic | Analyse mathématique ram Développements asymptotiques ram Perturbation (Mathématiques) ram Problèmes aux valeurs initiales ram Asymptotic expansions Initial value problems Mathematical analysis Perturbation (Mathematics) Korteweg-de-Vries-Gleichung (DE-588)4287203-0 gnd Anfangswertproblem (DE-588)4001991-3 gnd |
| topic_facet | Analyse mathématique Développements asymptotiques Perturbation (Mathématiques) Problèmes aux valeurs initiales Asymptotic expansions Initial value problems Mathematical analysis Perturbation (Mathematics) Korteweg-de-Vries-Gleichung Anfangswertproblem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015230854&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT kerffredde asymptoticanalysisofaclassofperturbedkortewegdevriesinitialvalueproblems |