New approaches to nonlinear waves:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham ; Heidelberg
Springer
[2016]
|
| Schriftenreihe: | Lecture notes in physics
volume 908 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 298 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 3319206893 9783319206899 9783319206905 |
Internformat
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| 020 | |a 9783319206899 |c pbk. |9 978-3-319-20689-9 | ||
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| 100 | 1 | |a Tobisch, Elena |d 1956- |0 (DE-588)142978663 |4 edt | |
| 245 | 1 | 0 | |a New approaches to nonlinear waves |c Elena Tobisch, editor |
| 264 | 1 | |a Cham ; Heidelberg |b Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a XV, 298 Seiten |b Illustrationen, Diagramme (teilweise farbig) | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Lecture notes in physics |v volume 908 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |o 10.1007/978-3-319-20690-5 |
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Datensatz im Suchindex
| _version_ | 1804175212064800768 |
|---|---|
| adam_text | Titel: New approaches to nonlinear waves
Autor: Tobisch, Elena
Jahr: 2016
Contents
Introduction.................................................................. 1
Elena Tobisch
1.1 Brief Historical Overview.............................................. 1
1.2 Main Notions............................................................ 3
1.2.1 Resonance Clusters............................................. 6
1.2.2 Power Law Energy Spectrum.................................. 7
1.2.3 Detuned Resonances............................................ 8
1.2.4 Summary........................................................ 10
1.3 Resonant Interactions................................................... 11
1.4 Modulation Instability.................................................. 13
1.5 Frameworks............................................................. 15
1.6 Reality Check........................................................... 16
References..................................................................... 17
The Effective Equation Method............................................ 21
Sergei Kuksin and Alberto Maiocchi
2.1 Introduction............................................................. 21
2.2 How to Construct the Effective Equation.............................. 22
2.3 Structure of Resonances................................................ 26
2.3.1 The Equations................................................... 27
2.3.2 Structure of Resonances for the NLS Equation............... 29
2.3.3 Structure of Resonances for CHM............................. 30
2.4 NLS: The Power-Law Energy Spectrum............................... 32
2.4.1 The Limit L- oo.............................................. 32
2.4.2 Power Law Spectra............................................. 37
2.5 CHM: Resonance Clustering........................................... 38
2.6 Concluding Remarks.................................................... 40
References..................................................................... 41
x Contents
3 On the Discovery of the Steady-State Resonant Water Waves.......... 43
Shijun Liao, Dali Xu, and Zeng Liu
3.1 Introduction............................................................. 44
3.2 Basic Ideas of Homotopy Analysis Method........................... 46
3.3 Steady-State Resonant Waves in Constant-Depth Water.............. 52
3.3.1 Mathematical Formulation..................................... 52
3.3.2 Steady-State Resonant Waves in Deep Water................. 59
3.3.3 Steady-State Resonant Waves in Finite Depth Water......... 69
3.4 Steady-State Class-I Bragg Resonant Waves.......................... 71
3.4.1 Mathematical Formulations.................................... 74
3.4.2 BriefResults.................................................... 75
3.5 Experimental Observation.............................................. 79
3.6 Concluding Remarks.................................................... 79
References..................................................................... 81
4 Modulational Instability in Equations of KdV Type..................... 83
Jared C. Bronski, Vera Mikyoung Hur, and Mathew A. Johnson
4.1 Introduction............................................................. 83
4.2 Periodic Traveling Waves of Generalized KdV Equations............ 85
4.2.1 Some Explicit Solutions........................................ 86
4.2.2 General Existence Theory...................................... 89
4.3 Formal Asymptotics and Whitham s Modulation Theory............. 92
4.3.1 Linear Dispersive Waves....................................... 92
4.3.2 Nonlinear Dispersive Waves ................................... 94
4.4 Rigorous Theory of Modulational Instability.......................... 98
4.4.1 Analytic Setup.................................................. 98
4.4.2 Modulational Instability in Generalized KdV Equations..... 101
4.4.3 Connection to Whitham Modulation Theory.................. 108
4.4.4 Evaluation of Am .............................................. 110
4.5 Applications............................................................. Ill
4.5.1 The KdV Equation.............................................. 112
4.5.2 The Modified KdV Equation................................... 113
4.5.3 The Schamel Equation.......................................... 115
4.5.4 Extensions to Equations with Nonlocal Dispersion........... 116
4.6 Concluding Remarks.................................................... 130
References..................................................................... 130
5 Modulational Instability and Rogue Waves in Shallow
Water Models................................................................. 135
R. Grimshaw, K.W. Chow, and H.N. Chan
5.1 Introduction............................................................. 135
5.2 Korteweg-de Vries Equations.......................................... 137
5.2.1 Modulational Instability........................................ 137
5.2.2 Breathers........................................................ 137
Contents
5.3 Boussinesq Model....................................................... 140
5.3.1 Modulational Instability........................................ 141
5.3.2 Breathers........................................................ 141
5.4 Hirota-Satsuma Model.................................................. 142
5.4.1 Modulational Instability........................................ 143
5.4.2 Breathers........................................................ 144
5.5 Discussion............................................................... 146
References..................................................................... 149
Hamiltonian Framework for Short Optical Pulses....................... 153
Shalva Amiranashvili
6.1 Introduction............................................................. 153
6.1.1 Ultrashort Pulses................................................ 153
6.1.2 Envelope Definition............................................. 155
6.2 Poisson Brackets........................................................ 161
6.2.1 Discrete Systems................................................ 161
6.2.2 Complex Variables.............................................. 165
6.2.3 One Continuous Field .......................................... 168
6.2.4 Canonical Bracket for Two Fields ............................. 171
6.2.5 GZF Bracket for Two Fields ................................... 173
6.3 Pulses in Optical Fibers................................................. 176
6.3.1 Problem Setting................................................. 177
6.3.2 Forward and Backward Waves................................. 179
6.3.3 Envelope Equations............................................. 180
6.4 Hamiltonian Description of Pulses..................................... 183
6.4.1 z-Propagation................................................... 184
6.4.2 z-Hamiltonian................................................... 185
6.4.3 Energy Transport............................................... 190
6.4.4 Photon Number................................................. 191
6.4.5 Analytic Signal................................................. 191
6.5 Concluding Remarks.................................................... 192
References..................................................................... 193
Modeling Water Waves Beyond Perturbations........................... 197
Didier Clamond and Denys Dutykh
7.1 Introduction............................................................. 197
7.2 Preliminaries............................................................ 199
7.3 Variational Formulations................................................ 200
7.4 Examples................................................................ 203
7.4.1 Shallow Water: Serre s Equations.............................. 203
7.4.2 Deep Water: Generalized Klein-Gordon Equations .......... 205
7.4.3 Arbitrary Depth................................................. 207
7.5 Discussion............................................................... 207
References..................................................................... 208
xii Contents
8 Quantitative Analysis of Nonlinear Water-Waves: A
Perspective of an Experimentalist.......................................... 211
Lev Shemer
8.1 Introduction............................................................. 211
8.2 The Experimental Facilities ............................................ 214
8.3 The Nonlinear Schrödinger Equation.................................. 215
8.4 The Modified Nonlinear Schrödinger (Dysthe) Equation............. 226
8.4.1 Formulation of Temporal and Spatial Evolution Problems... 226
8.4.2 Experiments on Spatial and Temporal Evolution
of Wave Groups Based on Digital Video Image
Processing....................................................... 230
8.4.3 Experimental Studies of Evolution of Peregrine Breather.... 239
8.5 The Spatial Zakharov Equation........................................ 245
8.5.1 The Model Equations........................................... 245
8.5.2 The Spatial Zakharov Equation vs. the Dysthe Model........ 248
8.5.3 Nonlinear Focusing Based on the Spatial
Zakharov Equation.............................................. 257
8.6 Statistics of Nonlinear Unidirectional Water Waves................... 269
8.7 Discussion and Conclusions............................................ 286
References..................................................................... 290
Index............................................................................... 295
|
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| id | DE-604.BV042913078 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:12:41Z |
| institution | BVB |
| isbn | 3319206893 9783319206899 9783319206905 |
| language | English |
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| physical | XV, 298 Seiten Illustrationen, Diagramme (teilweise farbig) |
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| publisher | Springer |
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| series2 | Lecture notes in physics |
| spelling | Tobisch, Elena 1956- (DE-588)142978663 edt New approaches to nonlinear waves Elena Tobisch, editor Cham ; Heidelberg Springer [2016] © 2016 XV, 298 Seiten Illustrationen, Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics volume 908 Erscheint auch als Online-Ausgabe 10.1007/978-3-319-20690-5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028340809&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | New approaches to nonlinear waves |
| title | New approaches to nonlinear waves |
| title_auth | New approaches to nonlinear waves |
| title_exact_search | New approaches to nonlinear waves |
| title_full | New approaches to nonlinear waves Elena Tobisch, editor |
| title_fullStr | New approaches to nonlinear waves Elena Tobisch, editor |
| title_full_unstemmed | New approaches to nonlinear waves Elena Tobisch, editor |
| title_short | New approaches to nonlinear waves |
| title_sort | new approaches to nonlinear waves |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028340809&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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