Nonlinear waves and solitons:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Tokyo
KTK Scientific Publ. u.a.
1989
|
| Schriftenreihe: | Mathematics and its applications / Japanese ser.
5. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Japan. übers. |
| Beschreibung: | XIV, 371 S. |
| ISBN: | 079230442X |
Internformat
MARC
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| 100 | 1 | |a Toda, Morikazu |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Hisenkei-hadō-to-soriton |
| 245 | 1 | 0 | |a Nonlinear waves and solitons |
| 264 | 1 | |a Tokyo |b KTK Scientific Publ. u.a. |c 1989 | |
| 300 | |a XIV, 371 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Japanese ser. |v 5. | |
| 500 | |a Aus d. Japan. übers. | ||
| 650 | 7 | |a Equation d'onde - Solutions numériques |2 ram | |
| 650 | 7 | |a Golffuncties |2 gtt | |
| 650 | 7 | |a Mathematische fysica |2 gtt | |
| 650 | 7 | |a Natuurkunde |2 gtt | |
| 650 | 7 | |a Niet-lineaire vergelijkingen |2 gtt | |
| 650 | 4 | |a Ondes non linéaires | |
| 650 | 7 | |a Ondes nonlinéaires |2 ram | |
| 650 | 4 | |a Solitons | |
| 650 | 7 | |a Solitons |2 gtt | |
| 650 | 7 | |a Solitons |2 ram | |
| 650 | 7 | |a Wiskundige methoden |2 gtt | |
| 650 | 4 | |a Équations d'onde - Solutions numériques | |
| 650 | 4 | |a Physik | |
| 650 | 4 | |a Nonlinear waves | |
| 650 | 4 | |a Solitons | |
| 650 | 4 | |a Wave equation |x Numerical solutions | |
| 650 | 0 | 7 | |a Soliton |0 (DE-588)4135213-0 |2 gnd |9 rswk-swf |
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| 689 | 3 | 0 | |a Soliton |0 (DE-588)4135213-0 |D s |
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| 810 | 2 | |a Japanese ser. |t Mathematics and its applications |v 5. |w (DE-604)BV000613779 |9 5 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-002550387 | ||
Datensatz im Suchindex
| _version_ | 1804118308820090880 |
|---|---|
| adam_text | CONTENTS
Series Editor s Preface v
Foreword vii
Chapter 1
Linear Waves 1
Sinusoidal Waves 1
Linear Lattice 3
Shallow Water Waves 6
Chapter 2
Surface Waves (1) 9
The Birth of Hydrodynamics 9
Trochoidal Waves 10
The Beginning of Water Tank Experiments 16
Euler s Equation of Motion 16
Chapter 3
Surface Waves (2) 21
Irrotational Motion 21
Irrotational Waves of Infinitely Deep Water 23
Wave Form 26
Drift of Water by Waves 28
Solitary Waves on Shallow Water 29
Chapter 4
The KdV Equation 35
Velocity Potential 35
Infinitesimal Shallow Water Waves (Linear Approximation) 37
Shallow Water Waves 39
Ordering of Small Quantities 42
The KdV Equation 43
ix
x Contents
Chapter 5
Particular Solutions of the KdV Equation 47
The Dimensionless KdV Equation 47
The Stationary Solution to the KdV Equation 48
Solitary Waves 50
Periodic Waves 53
Chapter 6
Two Soliton Solutions 57
The Two Soliton Solution 57
Asymptotic Forms 60
Motion of the Center of Mass of Solitons 62
Examples 65
Chapter 7
Supplements to Solitons 67
Historical Background 67
Discovery of the Soliton 69
Nonlinear Terms and Dispersion Terms 70
The KdV Case 72
Chapter 8
Solitons and Eigenvalues 75
Miura s Transformation 75
Trial and Error 78
The Eigenvalue Equation for the KdV 78
Eigenvalue of a Soliton 80
Eigenvalues of Two Soliton Solutions 81
Multi Soliton States and Motions Other Than Solitons 83
Chapter 9
Multi Soliton Solutions of the Schrodinger Equation 85
Eigenvalue Equations Associated with the KdV Equation 85
The Single Soliton Case 86
Solutions with Many Parameters 88
Other Propositions 91
Chapter 10
The Inverse Problem of the Schrodinger Equation 95
Wave Function and Potential 95
Continuous Spectrum 97
Scattering 97
Bound State 98
Contents xi
Inverse Problem 99
Supplementary Notes 101
Chapter 11
The Inverse Problem of the KdV Equation 107
Time Rate of Change of g 107
Time Dependence of Scattering Data Ill
Soliton Solution 114
Chapter 12
Non Linear Lattices 117
Computer Experiments by Fermi et al. 118
An Unexpected Result 118
Continuum Approximation 120
Derivation of the KdV Equation 122
Chapter 13
Dual Lattices 125
Equations of Motion 125
Dual Relations 127
Examples of Linear Lattices 129
LC Circuits 131
Chapter 14
Lattice Solitons 135
Exponential Interaction 135
Simple Solutions (Solitary Waves, Solitons) 139
The Two Soliton Solution 140
Collision of Solitons 143
Chapter 15
Conserved Quantities of Lattice Waves 149
Matrix Equation of Motion 149
Eigenvalues of the Matrix L 152
Unitary Equivalence 154
Conserved Quantities 157
Equations Associated with the Lattice 157
Chapter 16
Hirota s Method 163
Nonlinear Lattices 163
N Soliton Solutions 166
KdV Equation 169
xii Contents
Soliton Solution of the KdV Equation 171
Chapter 17
The Initial Value Problem of an Infinite Lattice 173
Infinite Lattices 174
Scattering Data 178
Discrete Integral Equation 179
Correspondence between Lattices and the KdV 181
Chapter 18
Multi Soliton Solutions 185
Multi Soliton Solutions 185
One Soliton Solution 190
Two Soliton Solution 194
Chapter 19
The Relation between Integrable Lattices and KdV Systems 197
Continuum Approximation 197
NS Transformation 200
The Soliton as an Example 203
Transformation of the Inverse Scattering Method 204
Chapter 20
Transformation between Two Lattices 209
The Kac Moerbeke System 210
Relation between the KM System and Lattices 211
The Backlund Transformation 212
Canonical Transformation 216
Chapter 21
Thermal Motion in the Lattice 219
Probability Distribution 219
Temperature and Pressure 221
Linear Lattices 222
Hard Sphere Systems 223
Nonlinear Lattices 225
Chapter 22
Lattice Cnoidal Waves 229
Harmonic Oscillators and Nonlinear Lattices 229
Equations of Motion 230
Elliptic Functions 231
The Soliton Solution 236
Contents xiii
Chapter 23
The ^ Function and Lattice Waves 239
Cnoidal Waves 239
Relation between Sinusoidal Waves and Solitons 242
^ Functions 245
The Addition Formula for #o00 and Cnoidal Waves 246
Supplement (Proof of (40)) 248
Chapter 24
Integrable and Non Integrable Systems 251
Three Particle Systems 251
Chaotic Motion 254
Exponential Lattices 258
Conserved Quantities of Three Particle Lattices 261
Chapter 25
Solution of the Three Particle Cyclic System 265
Letter of M. Kac 265
Spectrum of a Cyclic Three Particle System 266
Auxiliary Spectrum 269
Time Change of an Auxiliary Spectrum 273
Chapter 26
Method of Solving Cyclic Lattices (1) 277
Summary of the Results of the Preceding Chapter 277
Cyclic Lattices 278
The Discrete Hill s Equation 279
Discriminants 282
Auxiliary Spectrum 285
Chapter 27
Method of Solving Cyclic Lattices (2) 289
Rate of Change of Fundamental Solution q 290
Rate of Change of fi and the Discriminant 291
Rate of Change of Auxiliary Spectra 293
Integration of Auxiliary Spectra 295
The Case of g Gaps 296
Chapter 28
Inverse Spectral Problems and Solutions for Cyclic Systems 299
Riemann Surface 300
Multivariable ^ Function 302
Solution of a Cyclic Lattice 306
xiv Contents
Chapter 29
Examples of Cyclic Systems (1) 311
General Formulas 311
Example 1: A Cnoidal Wave 312
Example 2: Three Particle Systems 314
Integration by the General Method 317
Chapter 30
Examples of Cyclic Systems (2) 327
Solution by the General Method 327
Jacobian Elliptic Functions 330
Supplements 341
Bibliography 361
Index 367
|
| any_adam_object | 1 |
| author | Toda, Morikazu |
| author_facet | Toda, Morikazu |
| author_role | aut |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/4 |
| dewey-search | 530.1/4 |
| dewey-sort | 3530.1 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV004083305 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:08:14Z |
| institution | BVB |
| isbn | 079230442X |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002550387 |
| oclc_num | 20170241 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-355 DE-BY-UBR DE-11 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-739 DE-355 DE-BY-UBR DE-11 DE-188 DE-91G DE-BY-TUM |
| physical | XIV, 371 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | KTK Scientific Publ. u.a. |
| record_format | marc |
| series2 | Mathematics and its applications / Japanese ser. |
| spelling | Toda, Morikazu Verfasser aut Hisenkei-hadō-to-soriton Nonlinear waves and solitons Tokyo KTK Scientific Publ. u.a. 1989 XIV, 371 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Japanese ser. 5. Aus d. Japan. übers. Equation d'onde - Solutions numériques ram Golffuncties gtt Mathematische fysica gtt Natuurkunde gtt Niet-lineaire vergelijkingen gtt Ondes non linéaires Ondes nonlinéaires ram Solitons Solitons gtt Solitons ram Wiskundige methoden gtt Équations d'onde - Solutions numériques Physik Nonlinear waves Wave equation Numerical solutions Soliton (DE-588)4135213-0 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Soliton (DE-588)4135213-0 s Nichtlineare Wellengleichung (DE-588)4042104-1 s DE-604 Nichtlineare Welle (DE-588)4042102-8 s Wellengleichung (DE-588)4065315-8 s Numerisches Verfahren (DE-588)4128130-5 s Japanese ser. Mathematics and its applications 5. (DE-604)BV000613779 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002550387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Toda, Morikazu Nonlinear waves and solitons Equation d'onde - Solutions numériques ram Golffuncties gtt Mathematische fysica gtt Natuurkunde gtt Niet-lineaire vergelijkingen gtt Ondes non linéaires Ondes nonlinéaires ram Solitons Solitons gtt Solitons ram Wiskundige methoden gtt Équations d'onde - Solutions numériques Physik Nonlinear waves Wave equation Numerical solutions Soliton (DE-588)4135213-0 gnd Nichtlineare Welle (DE-588)4042102-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4135213-0 (DE-588)4042102-8 (DE-588)4128130-5 (DE-588)4042104-1 (DE-588)4065315-8 |
| title | Nonlinear waves and solitons |
| title_alt | Hisenkei-hadō-to-soriton |
| title_auth | Nonlinear waves and solitons |
| title_exact_search | Nonlinear waves and solitons |
| title_full | Nonlinear waves and solitons |
| title_fullStr | Nonlinear waves and solitons |
| title_full_unstemmed | Nonlinear waves and solitons |
| title_short | Nonlinear waves and solitons |
| title_sort | nonlinear waves and solitons |
| topic | Equation d'onde - Solutions numériques ram Golffuncties gtt Mathematische fysica gtt Natuurkunde gtt Niet-lineaire vergelijkingen gtt Ondes non linéaires Ondes nonlinéaires ram Solitons Solitons gtt Solitons ram Wiskundige methoden gtt Équations d'onde - Solutions numériques Physik Nonlinear waves Wave equation Numerical solutions Soliton (DE-588)4135213-0 gnd Nichtlineare Welle (DE-588)4042102-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Equation d'onde - Solutions numériques Golffuncties Mathematische fysica Natuurkunde Niet-lineaire vergelijkingen Ondes non linéaires Ondes nonlinéaires Solitons Wiskundige methoden Équations d'onde - Solutions numériques Physik Nonlinear waves Wave equation Numerical solutions Soliton Nichtlineare Welle Numerisches Verfahren Nichtlineare Wellengleichung Wellengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002550387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000613779 |
| work_keys_str_mv | AT todamorikazu hisenkeihadotosoriton AT todamorikazu nonlinearwavesandsolitons |