An introduction to asymmetric solitary waves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow, Essex
Longman Scientific & Technical
1991
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman monographs and surveys in pure and applied mathematics
56 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 280 S. graph. Darst. |
| ISBN: | 0582078148 |
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| 100 | 1 | |a Engelbrecht, Jurij K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to asymmetric solitary waves |c J. Engelbrecht |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman Scientific & Technical |c 1991 | |
| 300 | |a 280 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a équation différentielle hyperbolique |2 inriac | |
| 650 | 7 | |a équation évolution |2 inriac | |
| 650 | 4 | |a Differential equations, Hyperbolic | |
| 650 | 4 | |a Nonlinear waves | |
| 650 | 4 | |a Perturbation (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804119664549167104 |
|---|---|
| adam_text | Contents
Preface
Introduction 1
Chapter 1. Solitary waves and evolution equations 7
1.1. Solitary waves: a brief review 7
1.2. Evolution equations 16
1.2.1. Introduction 16
1.2.2. The iterative method 18
1.2.3. The asymptotic (reductive perturbation) method 21
1.2.4. The spectral method 23
1.2.5. Comparison of the methods 26
1.2.6. Remarks 33
1.3. Definitions 35
Chapter 2. Nonlinear conservative systems 44
2.1. The KdV equation 44
2.2. Inverse Scattering Transform (1ST) 51
2.3. Formation of solitons from initial data 60
2.3.1. Reflectionless potential 61
2.3.2. General form of a potential 73
2.3.3. Special forms of a potential 79
2.4. Discussion 91
2.4.1. Velocity of KdV solitons 91
2.4.2. Splitting of solitons 94
Chapter 3. Nonlinear systems perturbed by energy influx 98
3.1. Models 99
3.1.1. Physical description 99
3.1.2. Isolating the perturbed KdV equation 102
CONTENTS
3.2. Asymptotic analysis 107
3.2.1. Perturbative 1ST 107
3.2.2 Different types of energy influx 112
3.2.3. Direct perturbation 122
3.3. Numerical analysis 128
3.3.1. Computer simulation of amplitude equations 128
3.3.2. Stationary waves 134
3.3.3. Transient waves 141
Chapter 4. Nonlinear systems with essential energy influx 155
4.1. Models 156
4.1.1. Physical description 156
4.1.2. The Hodgkin Huxley model 158
4.1.3. The Lieberstein model 163
4.1.4. The FitzHugh Nagumo model 165
4.1.5. Other models 168
4.2. Evolution equations 171
4.2.1. The hyperbolic model and the basic evolution
equation 171
4.2.2. Full evolution equations 175
4.2.3. General remarks 180
4.3. Properties of evolution equations 183
4.3.1. Preliminary 183
4.3.2. Stationary waves, general analysis 184
4.3.3. Stationary waves, numerical results 206
4.3.4. Transient waves 218
4.4. Improved models 224
4.4.1. Dynamic nonlinearity 225
4.4.2. The recovery variable revisited 229
4.4.3. The van der Pol equation revisited 240
4.4.4. Development of models 246
4.5. Inverse problems 251
Closing remarks 258
Appendix: FFT technique for evolution equations (T. Peipman) 262
References 267
Index 278
|
| any_adam_object | 1 |
| author | Engelbrecht, Jurij K. |
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| id | DE-604.BV005454043 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:29:47Z |
| institution | BVB |
| isbn | 0582078148 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003412149 |
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| physical | 280 S. graph. Darst. |
| publishDate | 1991 |
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| publisher | Longman Scientific & Technical |
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| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Engelbrecht, Jurij K. Verfasser aut An introduction to asymmetric solitary waves J. Engelbrecht 1. publ. Harlow, Essex Longman Scientific & Technical 1991 280 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 56 Ondes non linéaires Ondes non linéaires ram Perturbation (Mathématiques) Perturbation (mathématiques) ram onde non linéaire inriac théorie perturbation inriac Équations différentielles hyperboliques Équations différentielles hyperboliques ram équation différentielle hyperbolique inriac équation évolution inriac Differential equations, Hyperbolic Nonlinear waves Perturbation (Mathematics) Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 s Störungstheorie (DE-588)4128420-3 s DE-604 Soliton (DE-588)4135213-0 s Pitman monographs and surveys in pure and applied mathematics 56 (DE-604)BV000022446 56 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003412149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Engelbrecht, Jurij K. An introduction to asymmetric solitary waves Pitman monographs and surveys in pure and applied mathematics Ondes non linéaires Ondes non linéaires ram Perturbation (Mathématiques) Perturbation (mathématiques) ram onde non linéaire inriac théorie perturbation inriac Équations différentielles hyperboliques Équations différentielles hyperboliques ram équation différentielle hyperbolique inriac équation évolution inriac Differential equations, Hyperbolic Nonlinear waves Perturbation (Mathematics) Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd Soliton (DE-588)4135213-0 gnd Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4228136-2 (DE-588)4135213-0 (DE-588)4128420-3 |
| title | An introduction to asymmetric solitary waves |
| title_auth | An introduction to asymmetric solitary waves |
| title_exact_search | An introduction to asymmetric solitary waves |
| title_full | An introduction to asymmetric solitary waves J. Engelbrecht |
| title_fullStr | An introduction to asymmetric solitary waves J. Engelbrecht |
| title_full_unstemmed | An introduction to asymmetric solitary waves J. Engelbrecht |
| title_short | An introduction to asymmetric solitary waves |
| title_sort | an introduction to asymmetric solitary waves |
| topic | Ondes non linéaires Ondes non linéaires ram Perturbation (Mathématiques) Perturbation (mathématiques) ram onde non linéaire inriac théorie perturbation inriac Équations différentielles hyperboliques Équations différentielles hyperboliques ram équation différentielle hyperbolique inriac équation évolution inriac Differential equations, Hyperbolic Nonlinear waves Perturbation (Mathematics) Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd Soliton (DE-588)4135213-0 gnd Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Ondes non linéaires Perturbation (Mathématiques) Perturbation (mathématiques) onde non linéaire théorie perturbation Équations différentielles hyperboliques équation différentielle hyperbolique équation évolution Differential equations, Hyperbolic Nonlinear waves Perturbation (Mathematics) Nichtlineare hyperbolische Differentialgleichung Soliton Störungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003412149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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