Waves called solitons: concepts and experiments
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Edition: | 3., rev. and enl. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 307 - 323 |
| Physical Description: | XIX, 327 S. Ill., graph. Darst. |
| ISBN: | 3540659196 |
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| 245 | 1 | 0 | |a Waves called solitons |b concepts and experiments |c Michel Remoissenet |
| 250 | |a 3., rev. and enl. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIX, 327 S. |b Ill., graph. Darst. | ||
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| adam_text | XIII CONTENTS 1 BASIC CONCEPTS AND THE DISCOVERY OF SOLITONS
.................... 1 1.1 A LOOK AT LINEAR AND NONLINEAR
SIGNATURES............................. 1 1.2 DISCOVERY OF THE SOLITARY
WAVE ........................................ 3 1.3 DISCOVERY OF THE
SOLITON ................................................ 7 1.4 THE
SOLITON CONCEPT IN PHYSICS ........................................ 11 2
LINEAR WAVES IN ELECTRICAL TRANSMISSION LINES ................... 12 2.1
LINEAR NONDISPERSIVE WAVES ...........................................
12 2.2 SINUSOIDAL-WAVE CHARACTERISTICS
....................................... 15 2.2.1 WAVE ENERGY DENSITY AND
POWER........................... 18 2.3 THE GROUP-VELOCITY CONCEPT
............................................ 19 2.4 LINEAR DISPERSIVE
WAVES................................................ 21 2.4.1
DISPERSIVE TRANSMISSION LINES .............................. 21 2.4.2
ELECTRICAL NETWORK ........................................... 23 2.4.3
THE WEAKLY DISPERSIVE LIMIT ................................ 26 2.5
EVOLUTION OF A WAVEPACKET ENVELOPE.................................. 27
2.6 DISPERSION-INDUCED WAVEPACKET BROADENING......................... 31
APPENDIX 2A. GENERAL SOLUTION FOR THE ENVELOPE EVOLUTION..............
34 APPENDIX 2B. EVOLUTION OF THE ENVELOPE OF A GAUSSIAN WAVEPACKET. . .
35 3 SOLITONS IN NONLINEAR TRANSMISSION LINES ..........................
37 3.1 NONLINEAR AND DISPERSIONLESS TRANSMISSION LINES
.................... 37 3.2 COMBINED EFFECTS OF DISPERSION AND
NONLINEARITY.................... 41 3.3 ELECTRICAL SOLITARY WAVES AND
PULSE SOLITONS.......................... 42 3.4 LABORATORY EXPERIMENTS
ON PULSE SOLITONS............................ 46 3.4.1 EXPERIMENTAL
ARRANGEMENT.................................. 46 3.4.2 SERIES OF
EXPERIMENTS ....................................... 48 3.5 EXPERIMENTS
WITH A POCKET VERSION OF THE ELECTRICAL NETWORK....... 52 XIV 3.6
NONLINEAR TRANSMISSION LINES IN THE MICROWAVE RANGE .............. 56
APPENDIX 3A. CALCULATION OF THE EFFECT OF NONLINEARITY ON WAVE
PROPAGATION ....................................... 58 APPENDIX 3B.
DERIVATION OF THE SOLITARY-WAVE SOLUTION ................ 60 APPENDIX
3C. DERIVATION OF THE KDV EQUATION AND ITS SOLITON SOLUTION 62 APPENDIX
3D. DETAILS OF THE ELECTRONICS: SWITCH DRIVER AND PULSE GENERATOR
......................... 64 4 MORE ON TRANSMISSION-LINE SOLITONS
................................. 65 4.1 LATTICE SOLITONS IN THE
ELECTRICAL TODA NETWORK ...................... 65 4.1.1 LATTICE
SOLITONS............................................... 67 4.2
EXPERIMENTS ON LATTICE SOLITONS ........................................
68 4.2.1 COLLISIONS OF TWO LATTICE SOLITONS MOVING IN OPPOSITE
DIRECTIONS.............................. 70 4.2.2 THE FERMI-PASTA-ULAM
RECURRENCE PHENOMENON......... 70 4.3 PERIODIC WAVETRAINS IN
TRANSMISSION LINES ............................ 71 4.3.1 THE SOLITARY
WAVE LIMIT AND SINUSOIDAL LIMIT OF THE CNOIDAL
WAVE.......................................... 72 4.4 MODULATED WAVES
AND THE NONLINEAR DISPERSION RELATION ............ 72 4.5 ENVELOPE AND
HOLE SOLITONS ........................................... 74 4.5.1
EXPERIMENTS ON ENVELOPE AND HOLE SOLITONS .............. 76 4.6
MODULATIONAL
INSTABILITY................................................. 77 4.7
LABORATORY EXPERIMENTS ON MODULATIONAL INSTABILITY ................ 82
4.7.1 MODEL EQUATIONS ............................................. 82
4.7.2 EXPERIMENTS.................................................. 84
4.8 MODULATIONAL INSTABILITY OF TWO COUPLED WAVES......................
86 4.9 MICROWAVE SOLITONS IN MAGNETIC TRANSMISSION
LINES.................. 88 4.9.1 NONLINEAR SPIN
WAVES........................................ 88 4.9.2 NLS MODEL
EQUATION FOR SPIN WAVES....................... 88 4.9.3 OBSERVATION OF
MAGNETIC ENVELOPE SOLITONS................ 89 4.10 SOLITONS AND SIGNAL
PROCESSING.......................................... 91 APPENDIX 4A.
PERIODIC WAVETRAIN SOLUTIONS ............................... 93 APPENDIX
4B. THE JACOBI ELLIPTIC FUNCTIONS................................ 95
4B.1 ASYMPTOTIC LIMITS............................................ 96
4B.2 DERIVATIVES AND INTEGRALS.................................... 98
APPENDIX 4C. ENVELOPE AND HOLE SOLITON SOLUTIONS.......................
98 XV 5 HYDRODYNAMIC SOLITONS
................................................... 103 5.1 EQUATIONS
FOR SURFACE WATER WAVES.................................... 103 5.1.1
REDUCED FLUID EQUATIONS ................................ . . . 104 5.2
SMALL-AMPLITUDE SURFACE GRAVITY WAVES............................... 100
5.3 LINEAR SHALLOW- AND DEEP-WATER WAVES...............................
108 5.3.1 SHALLOW-WATER WAVES .......................................
108 5.3.2 DEEP-WATER WAVES ..........................................
109 5.4 SURFACE-TENSION EFFECTS: CAPILLARY WAVES
............................. 110 5.5 SOLITONS IN SHALLOW WATER
.............................................. 112 5.6 EXPERIMENTS ON
SOLITONS IN SHALLOW WATER ........................... 115 5.6.1
EXPERIMENTAL ARRANGEMENT.................................. 116 5.6.2
EXPERIMENTS.................................................. 116 5.7
STOKES WAVES AND SOLITON WAVEPACKETS IN DEEP WATER .............. 120
5.7.1 STOKES WAVES ................................................ 120
5.7.2 SOLITON WAVEPACKETS ........................................ 121
5.7.3 EXPERIMENTS ON SOLITONS IN DEEP WATER ................... 122 5.8
EXPERIMENTS ON MODULATIONAL INSTABILITY IN DEEP WATER ............ 123
5.9 SOME APPLICATIONS OF THE KDV MODEL..................................
126 5.9.1 BLOOD PRESSURE WAVE PROPAGATION.........................126
5.9.2 NONLINEAR MODES OF LIQUID DROPS...........................127
APPENDIX 5A. BASIC EQUATIONS OF FLUID MECHANICS.......................
127 5A.1 CONSERVATION OF MASS....................................... 127
5A.2 CONSERVATION OF MOMENTUM................................ 129 5A.3
CONSERVATION OF ENTROPY.................................... 130 APPENDIX
5B. BASIC DEFINITIONS AND APPROXIMATIONS..................... 130 5B.1
STREAMLINE .................................................... 130 5B.2
IRROTATIONAL AND INCOMPRESSIBLE FLOW ..................... 131 5B.3
TWO-DIMENSIONAL FLOW: THE STREAM FUNCTION.............. 132 5B.4
BOUNDARY CONDITIONS........................................ 134 5B.5
SURFACE TENSION .............................................. 135
APPENDIX 5C. DERIVATION OF THE KDV EQUATION: THE PERTURBATIVE
APPROACH................................... 136 APPENDIX 5D. DERIVATION
OF THE NONLINEAR DISPERSION RELATION........... 139 APPENDIX 5E. DETAILS
OF THE PROBES AND THE ELECTRONICS.................. 142 XVI 6 MECHANICAL
SOLITONS ........................................................ 143
6.1 AN EXPERIMENTAL MECHANICAL TRANSMISSSION LINE .....................
143 6.1.1 GENERAL DESCRIPTION OF THE LINE .............................
143 6.1.2 CONSTRUCTION OF THE LINE.....................................
145 6.2 MECHANICAL KINK SOLITONS
............................................... 145 6.2.1 LINEAR WAVES
IN THE LOW-AMPLITUDE LIMIT.................. 146 6.2.2 LARGE AMPLITUDE
WAVES: KINK SOLITONS..................... 147 6.2.3 LORENTZ CONTRACTION
OF THE KINK SOLITONS .................. 149 6.3 PARTICLE PROPERTIES OF
THE KINK SOLITONS................................ 151 6.4 KINK*KINK AND
KINK*ANTIKINK COLLISIONS.............................. 152 6.5 BREATHER
SOLITONS ........................................................ 154
6.6 EXPERIMENTS ON KINKS AND BREATHERS .................................
156 6.7 HELICAL WAVES, OR KINK
ARRAY........................................... 157 6.8 DISSIPATIVE
EFFECTS....................................................... 159 6.9
ENVELOPE SOLITONS
....................................................... 161 6.10 LATTICE
EFFECTS.............................................................163
6.10.1 POCKET VERSION OF THE PENDULUM CHAIN, LATTICE EFFECTS....163
6.10.2 PENDULUM CHAIN WITH WEAK COUPLING....................... 164 6.11
A MECHANICAL TRANMSISSION LINE WITH TWO EQUILIBRIUM STATES........165
6.11.1 PERIODIC AND DOUBLE-WELL SUBSTRATE POTENTIALS............. 165
6.11.2 GENERAL DESCRIPTION OF THE MECHANICAL CHAIN..............166
6.11.3 KINK-SOLITON SOLUTIONS.......................................169
6.11.4 COMPACTON-LIKE KINKS OR COMPACTONS...................... 170
6.11.5 EXPERIMENTS...................................................
173 6.12 SOLITONS, COMPACTONS AND
NANOPTERONS................................ 175 APPENDIX 6A.
KINK-SOLITON AND ANTIKINK-SOLITON SOLUTIONS.............. 178 APPENDIX
6B. CALCULATION OF THE ENERGY AND THE MASS OF A KINK SOLITON
............................. 179 APPENDIX 6C. SOLUTIONS FOR KINK * KINK
AND KINK * ANTIKINK COLLISIONS, AND BREATHERS................... 180
6C.1 KINK SOLUTIONS ............................................... 182
6C.2 KINK*KINK COLLISIONS........................................ 182
6C.3 BREATHER SOLITONS............................................. 183
6C.4 KINK*ANTIKINK COLLISION..................................... 184
APPENDIX 6D. SOLUTIONS FOR HELICAL
WAVES................................. 185 APPENDIX 6E. PENDULUM WITH
TORSION AND GRAVITY........................187 XVII APPENDIX 6F MODEL
EQUATION FOR THE PENDULUM CHAIN...................187 7 FLUXONS IN
JOSEPHSON TRANSMISSION LINES ......................... 189 7.1 THE
JOSEPHSON EFFECT IN A SHORT JUNCTION ............................. 189
7.1.1 THE SMALL JOSEPHSON JUNCTION ............................. 190 7.2
THE LONG JOSEPHSON JUNCTION AS A TRANSMISSION LINE ................ 192
7.3 DISSIPATIVE EFFECTS
...................................................... 196 7.4
EXPERIMENTAL OBSERVATIONS OF FLUXONS ................................
198 7.4.1 INDIRECT OBSERVATION .........................................
198 7.4.2 DIRECT OBSERVATION ..........................................
199 7.4.3 LATTICE EFFECTS
................................................ 201 APPENDIX 7A.
JOSEPHSON EQUATIONS ....................................... 201 8
SOLITONS IN OPTICAL FIBERS
................................................ 203 8.1 OPTICAL-FIBER
CHARACTERISTICS ............................................ 203 8.1.1
LINEAR DISPERSIVE EFFECTS.................................... 204 8.1.2
NONLINEAR EFFECTS ............................................ 206 8.1.3
EFFECT OF LOSSES .............................................. 207 8.2
WAVE-ENVELOPE PROPAGATION ...........................................
208 8.3 BRIGHT AND DARK SOLITONS
............................................... 210 8.3.1 BRIGHT
SOLITONS ............................................... 211 8.3.2 DARK
SOLITONS................................................. 213 8.4
EXPERIMENTS ON OPTICAL SOLITONS .......................................
214 8.5 PERTURBATIONS AND SOLITON
COMMUNICATIONS........................... 216 8.5.1 EFFECT OF LOSSES
.............................................. 216 8.5.2 SOLITON
COMMUNICATIONS .................................... 217 8.6 MODULATIONAL
INSTABILITY OF COUPLED WAVES ........................... 218 8.7 A LOOK
AT QUANTUM-OPTICAL SOLITONS................................... . 219 8.8
SOME OTHER KINDS OF OPTICAL SOLITONS: SPATIAL SOLITONS................
221 APPENDIX 8A. ELECTROMAGNETIC EQUATIONS IN A NONLINEAR MEDIUM.......
222 9 THE SOLITON CONCEPT IN LATTICE DYNAMICS
........................... 225 9.1 THE ONE-DIMENSIONAL LATTICE IN THE
CONTINUUM APPROXIMATION...... 225 9.2 THE QUASI-CONTINUUM APPROXIMATION
FOR THE MONATOMIC LATTICE.... 230 9.3 THE TODA LATTICE
......................................................... 232 9.4
ENVELOPE SOLITONS AND LOCALIZED MODES............................... 233
XVIII 9.5 THE ONE-DIMENSIONAL LATTICE WITH TRANSVERSE NONLINEAR MODES
.... 235 9.6 MOTION OF DISLOCATIONS IN A ONE-DIMENSIONAL CRYSTAL
................ 238 9.7 THE ONE-DIMENSIONAL LATTICE MODEL FOR
STRUCTURAL PHASE TRANSITIONS.........................................
239 9.7.1 THE ORDER*DISORDER TRANSITION ..............................
241 9.7.2 THE DISPLACIVE TRANSITION....................................
242 9.8 KINK-SOLITON SOLUTIONS FOR GENERALIZED ON-SITE
POTENTIALS........... 244 9.9 A LATTICE MODEL WITH AN EXACT KINK-SOLITON
SOLUTION..................247 9.10 ENERGY LOCALIZATION IN NONLINEAR
LATTICES. ............................. 250 9.10.1 SELF-TRAPPED STATES:
POLARON AND CONFORMON.................. 250 9.10.2 INTRINSIC LOCALIZED
MODES OR DISCRETE BREATHERS............... 251 9.11 OBSERVATION OF
DISCRETE BREATHERS....................................... 253 9.11.1
DISCRETE PENDULUM CHAINS......................................253 9.11.2
MECHANICAL CHAIN WITH TORSION AND GRAVITY...................254 9.11.3 A
CHAIN OF MAGNETIC PENDULUMS...............................256 APPENDIX
9A. SOLUTIONS FOR TRANSVERSE DISPLACEMENTS ................... 257
APPENDIX 9B. KINK-SOLITON OR DOMAIN-WALL SOLUTIONS ...................
259 APPENDIX 9C CONSTRUCTION OF A DOUBLE-WELL
POTENTIAL.................... 260 10 A LOOK AT SOME REMARKABLE
MATHEMATICAL TECHNIQUES ........ 262 10.1 LAX EQUATIONS AND THE INVERSE
SCATTERING TRANSFORM METHOD........ 262 10.1.1 THE FOURIER-TRANSFORM
METHOD FOR LINEAR EQUATIONS ..... 263 10.1.2 THE LAX PAIR FOR NONLINEAR
EVOLUTION EQUATIONS.......... 264 10.2 THE KDV EQUATION AND THE SPECTRAL
PROBLEM ......................... 266 10.3 TIME EVOLUTION OF THE
SCATTERING DATA.................................. 267 10.3.1 DISCRETE
EIGENVALUES......................................... 267 10.3.2
CONTINUOUS SPECTRUM ....................................... 269 10.4 THE
INVERSE SCATTERING PROBLEM ........................................ 270
10.4.1 DISCRETE SPECTRUM ONLY: SOLITON SOLUTION.................. 271
10.5 RESPONSE OF THE KDV MODEL TO AN INITIAL DISTURBANCE ..............
273 10.5.1 THE DELTA FUNCTION POTENTIAL ................................
273 10.5.2 THE RECTANGULAR POTENTIAL WELL..............................
274 10.5.3 THE SECH-SQUARED POTENTIAL WELL ...........................
274 10.6 THE INVERSE SCATTERING TRANSFORM FOR THE NLS
EQUATION............. 275 10.7 THE HIROTA METHOD FOR THE KDV EQUATION
............................ 277 10.8 THE HIROTA METHOD FOR THE NLS
EQUATION ............................ 280 XIX 1 1 DIFFUSIVE SOLITONS
............................................................ 284 11.1
COMBINED EFFECTS OF DISSIPATION AND NONLINEARITY ................... 285
11.1.1 A DIFFUSIVE ELECTRICAL TRANSMISSION LINE.................... 285
11.1.2 LINEAR DIFFUSIVE WAVES...................................... 287
11.1.3 KINK-SHAPED DIFFUSIVE SOLITONS.............................288
11.1.4 EXPERIMENTS ON ELECTRICAL DIFFUSIVE SOLITONS............... 290
11.2 REACTION DIFFUSION PROCESSES
.......................................... 291 11.2.1 REACTION DIFFUSION
EQUATIONS................................ 291 11.2.2 A CHEMICAL MODEL
WITH REACTION DIFFUSION.................293 11.2.3 AN ELECTRICAL LATTICE
WITH REACTION DIFFUSION................296 11.2.4 EXPERIMENTS WITH AN
ELECTRICAL LATTICE......................298 11.3 A MECHANICAL ANALOG
WITH DIFFUSIVE SOLITONS......................... 299 11.3.1 CHAIN WITH
FLEXION AND GRAVITY............................. 299 11.3.2 EXPERIMENTAL
CHAIN .......................................... 300 11.4 REACTION
DIFFUSION PROCESSES IN LATTICES............................... 301
11.4.1 PROPAGATION FAILURE ......................................... 301
11.4.2 DISCRETE REACTION DIFFUSION MODEL WITH EXACT SOLUTION... 302
APPENDIX 11A. DERIVATION OF THE BURGERS EQUATION.
........................ 303 APPENDIX 11B. SOLUTION OF THE REACTION
DIFFUSION EQUATION.................304 APPENDIX 11C. EQUATION OF MOTION
OF AN EULER STRUT........................305 REFERENCES
............................................................................
307 SUBJECT INDEX
........................................................................
325 XX
|
| any_adam_object | 1 |
| author | Remoissenet, Michel 1935- |
| author_GND | (DE-588)121031543 |
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| ctrlnum | (OCoLC)41355638 (DE-599)BVBBV012608373 |
| dewey-full | 531/.1133 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.1133 |
| dewey-search | 531/.1133 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV012608373 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:30:32Z |
| institution | BVB |
| isbn | 3540659196 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008563566 |
| oclc_num | 41355638 |
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| physical | XIX, 327 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| spelling | Remoissenet, Michel 1935- Verfasser (DE-588)121031543 aut Waves called solitons concepts and experiments Michel Remoissenet 3., rev. and enl. ed. Berlin [u.a.] Springer 1999 XIX, 327 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 307 - 323 Solitons (congressos) larpcal Solitons Soliton (DE-588)4135213-0 gnd rswk-swf Soliton (DE-588)4135213-0 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Remoissenet, Michel 1935- Waves called solitons concepts and experiments Solitons (congressos) larpcal Solitons Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4135213-0 |
| title | Waves called solitons concepts and experiments |
| title_auth | Waves called solitons concepts and experiments |
| title_exact_search | Waves called solitons concepts and experiments |
| title_full | Waves called solitons concepts and experiments Michel Remoissenet |
| title_fullStr | Waves called solitons concepts and experiments Michel Remoissenet |
| title_full_unstemmed | Waves called solitons concepts and experiments Michel Remoissenet |
| title_short | Waves called solitons |
| title_sort | waves called solitons concepts and experiments |
| title_sub | concepts and experiments |
| topic | Solitons (congressos) larpcal Solitons Soliton (DE-588)4135213-0 gnd |
| topic_facet | Solitons (congressos) Solitons Soliton |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT remoissenetmichel wavescalledsolitonsconceptsandexperiments |