Physics of solitons:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English French |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
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| Edition: | Engl. ed., 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 422 S. Ill., graph. Darst. |
| ISBN: | 0521854210 9780521854214 |
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| 250 | |a Engl. ed., 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
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Record in the Search Index
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| adam_text | Titel: Physics of solitons
Autor: Dauxois, Thierry
Jahr: 2006
Contents
List of Portraits
Preface
page ix
xi
Part I Different classes of solitons
Introduction 1
1 Nontopological solitons: the Korteweg-de Vries equation 7
1.1 The discovery 7
1.2 The solutions of the KdV equation 17
1.3 Conservation rules 23
1.4 Nonlinear electrical lines 25
1.5 Blood pressure waves 33
1.6 Internal waves in oceanography 38
1.7 Generality of the KdV equation 39
2 Topological solitons: the sine-Gordon equation 42
2.1 A simple mechanical example: the chain of coupled pendula 42
2.2 Solutions of the sine-Gordon equation 44
2.3 Long Josephson junctions 60
2.4 Other examples of topological solitons 70
3 Envelope solitons and nonlinear localisation: the nonlinear
Schrödinger equation 75
3.1 Nonlinear waves in the pendulum chain: the NLS equation 75
3.2 Properties of the nonlinear Schrödinger equation 80
3.3 Conservation laws 90
3.4 Ncether s theorem 94
3.5 Nonlinear electrical lines 96
3.6 Solitons in optical fibres 98
3.7 Self-focusing in optics: the NLS equation in two space dimensions 112
3.8 Conclusion 116
vi Contents
4 The modelling process: ion acoustic waves in a plasma 117
4.1 Introduction 117
4.2 The plasma 118
4.3 Study of the linear dynamics 122
4.4 Nonlinear study 124
4.5 Derivation of the nonlinear Schrödinger equation 127
4.6 Experimental observations 130
4.7 Discussion 133
Part II Mathematical methods for the study of solitons
Introduction 139
5 Linearisation around the soliton solution 141
5.1 Spectrum of the excitations around a sine-Gordon soliton 141
5.2 Application: perturbation of a soliton 144
5.3 Spectrum of the excitations around a Ø4 soliton 150
6 Collective coordinate method 156
6.1 sine-Gordon soliton interacting with an impurity: effective
Lagrangian method 156
6.2 Improving the method with a second collective coordinate 160
7 The inverse-scattering transform 165
7.1 Inverse scattering transform for the KdV equation 165
7.2 The inverse scattering transform: a nonlinear Fourier analysis 175
Part III Examples in solid state and atomic physics
Introduction 185
8 The Fermi-Pasta-Ulam problem 187
8.1 The physical question 187
8.2 Fermi, Pasta and Ulam: the characters 189
8.3 The solution of the FPU problem 192
8.4 Kruskal and Zabusky: the pioneers 195
8.5 FPU and the Japanese School 197
9 A simple model for dislocations in crystals 199
9.1 Plastic deformation of crystals 199
9.2 A one-dimensional model: the Frenkel-Kontorova model 202
9.3 Continuum limit approximation: the sine-Gordon equation 204
9.4 Are dislocations solitons? 205
9.5 Applications 208
10 Ferroelectric domain walls 211
10.1 Ferroelectric materials 211
10.2 A one-dimensional ferroelectric model 214
Contents vii
10.3 Structure of the domain walls in the continuum limit
approximation 216
10.4 Dielectric response of a ferroelectric material 220
10.5 Thermodynamics of a nonlinear system 223
11 Incommensurate phases 235
11.1 Examples in solid state physics 235
11.2 A one-dimensional model for incommensurate phases: the
Frenkel-Kontorova model 236
11.3 Commensurate phases 237
11.4 The commensurate-incommensurate transition 238
11.5 Structure of the incommensurate phase 239
11.6 Calculation of 8C 240
11.7 Phase diagram 243
11.8 Dynamics of the incommensurate phase 245
11.9 Formation of the discommensurations 247
11.10 Conclusion 250
12 Solitons in magnetic systems 252
12.1 Ferromagnetism and antiferromagnetism 252
12.2 Equations for the dynamics of a spin chain 254
12.3 Magnons and solitons 257
12.4 Validity of the sine-Gordon approximation 261
12.5 Solitons in antiferromagnetic spin chains 267
12.6 Conclusion 268
13 Solitons in conducting polymers 269
13.1 Materials 269
13.2 The physical model of poly acetylene 272
13.3 The ground state of poly acetylene 274
13.4 The excited state of polyacetylene: the soliton solution 283
13.5 Mechanism of electric conduction in conducting polyacetylene 287
13.6 An experimental test for the presence of solitons 292
13.7 The other nonlinear excitations of polyacetylene 295
14 Solitons in Bose-Einstein condensates 297
14.1 Introduction 297
14.2 Theoretical description of a condensate 299
14.3 Magnetic traps 305
14.4 Dynamic properties 306
14.5 Soliton solutions 312
Part IV Nonlinear excitations in biological molecules
Introduction 323
viii Contents
15 Energy localisation and transfer in proteins 326
15.1 The mechanism proposed by Davydov 326
15.2 The Davydov equations 341
15.3 Does the Davydov soliton exist? 343
15.4 A model physical system: the acetanilide crystal 345
16 Nonlinear dynamics and statistical physics of DNA 351
16.1 A simple DNA model 351
16.2 Nonlinear dynamics of DNA 362
16.3 Statistical physics of DNA thermal denaturation 370
16.4 Stability of a domain wall: another approach to denaturation 377
Conclusion Physical solitons: do they exist? 389
Part V Appendices
A Derivation of the KdV equation for surface hydrodynamic waves 395
A. 1 Basic equations and boundary conditions 395
A.2 Mathematical formulation of the problem 397
A.3 The linear limit 401
A.4 The nonlinear equation in shallow water 402
B Mechanics of a continuous medium 405
B.l Lagrangian formalism 405
B.2 Hamiltonian formalism 407
C Coherent states of a harmonic oscillator 409
References 412
Index 421
|
| adam_txt |
Titel: Physics of solitons
Autor: Dauxois, Thierry
Jahr: 2006
Contents
List of Portraits
Preface
page ix
xi
Part I Different classes of solitons
Introduction 1
1 Nontopological solitons: the Korteweg-de Vries equation 7
1.1 The discovery 7
1.2 The solutions of the KdV equation 17
1.3 Conservation rules 23
1.4 Nonlinear electrical lines 25
1.5 Blood pressure waves 33
1.6 Internal waves in oceanography 38
1.7 Generality of the KdV equation 39
2 Topological solitons: the sine-Gordon equation 42
2.1 A simple mechanical example: the chain of coupled pendula 42
2.2 Solutions of the sine-Gordon equation 44
2.3 Long Josephson junctions 60
2.4 Other examples of topological solitons 70
3 Envelope solitons and nonlinear localisation: the nonlinear
Schrödinger equation 75
3.1 Nonlinear waves in the pendulum chain: the NLS equation 75
3.2 Properties of the nonlinear Schrödinger equation 80
3.3 Conservation laws 90
3.4 Ncether's theorem 94
3.5 Nonlinear electrical lines 96
3.6 Solitons in optical fibres 98
3.7 Self-focusing in optics: the NLS equation in two space dimensions 112
3.8 Conclusion 116
vi Contents
4 The modelling process: ion acoustic waves in a plasma 117
4.1 Introduction 117
4.2 The plasma 118
4.3 Study of the linear dynamics 122
4.4 Nonlinear study 124
4.5 Derivation of the nonlinear Schrödinger equation 127
4.6 Experimental observations 130
4.7 Discussion 133
Part II Mathematical methods for the study of solitons
Introduction 139
5 Linearisation around the soliton solution 141
5.1 Spectrum of the excitations around a sine-Gordon soliton 141
5.2 Application: perturbation of a soliton 144
5.3 Spectrum of the excitations around a Ø4 soliton 150
6 Collective coordinate method 156
6.1 sine-Gordon soliton interacting with an impurity: effective
Lagrangian method 156
6.2 Improving the method with a second collective coordinate 160
7 The inverse-scattering transform 165
7.1 Inverse scattering transform for the KdV equation 165
7.2 The inverse scattering transform: a'nonlinear Fourier analysis' 175
Part III Examples in solid state and atomic physics
Introduction 185
8 The Fermi-Pasta-Ulam problem 187
8.1 The physical question 187
8.2 Fermi, Pasta and Ulam: the characters 189
8.3 The solution of the FPU problem 192
8.4 Kruskal and Zabusky: the pioneers 195
8.5 FPU and the Japanese School 197
9 A simple model for dislocations in crystals 199
9.1 Plastic deformation of crystals 199
9.2 A one-dimensional model: the Frenkel-Kontorova model 202
9.3 Continuum limit approximation: the sine-Gordon equation 204
9.4 Are dislocations solitons? 205
9.5 Applications 208
10 Ferroelectric domain walls 211
10.1 Ferroelectric materials 211
10.2 A one-dimensional ferroelectric model 214
Contents vii
10.3 Structure of the domain walls in the continuum limit
approximation 216
10.4 Dielectric response of a ferroelectric material 220
10.5 Thermodynamics of a nonlinear system 223
11 Incommensurate phases 235
11.1 Examples in solid state physics 235
11.2 A one-dimensional model for incommensurate phases: the
Frenkel-Kontorova model 236
11.3 Commensurate phases 237
11.4 The commensurate-incommensurate transition 238
11.5 Structure of the incommensurate phase 239
11.6 Calculation of 8C 240
11.7 Phase diagram 243
11.8 Dynamics of the incommensurate phase 245
11.9 Formation of the discommensurations 247
11.10 Conclusion 250
12 Solitons in magnetic systems 252
12.1 Ferromagnetism and antiferromagnetism 252
12.2 Equations for the dynamics of a spin chain 254
12.3 Magnons and solitons 257
12.4 Validity of the sine-Gordon approximation 261
12.5 Solitons in antiferromagnetic spin chains 267
12.6 Conclusion 268
13 Solitons in conducting polymers 269
13.1 Materials 269
13.2 The physical model of poly acetylene 272
13.3 The ground state of poly acetylene 274
13.4 The excited state of polyacetylene: the soliton solution 283
13.5 Mechanism of electric conduction in conducting polyacetylene 287
13.6 An experimental test for the presence of solitons 292
13.7 The other nonlinear excitations of polyacetylene 295
14 Solitons in Bose-Einstein condensates 297
14.1 Introduction 297
14.2 Theoretical description of a condensate 299
14.3 Magnetic traps 305
14.4 Dynamic properties 306
14.5 Soliton solutions 312
Part IV Nonlinear excitations in biological molecules
Introduction 323
viii Contents
15 Energy localisation and transfer in proteins 326
15.1 The mechanism proposed by Davydov 326
15.2 The Davydov equations 341
15.3 Does the Davydov soliton exist? 343
15.4 A model physical system: the acetanilide crystal 345
16 Nonlinear dynamics and statistical physics of DNA 351
16.1 A simple DNA model 351
16.2 Nonlinear dynamics of DNA 362
16.3 Statistical physics of DNA thermal denaturation 370
16.4 Stability of a domain wall: another approach to denaturation 377
Conclusion Physical solitons: do they exist? 389
Part V Appendices
A Derivation of the KdV equation for surface hydrodynamic waves 395
A. 1 Basic equations and boundary conditions 395
A.2 Mathematical formulation of the problem 397
A.3 The linear limit 401
A.4 The nonlinear equation in shallow water 402
B Mechanics of a continuous medium 405
B.l Lagrangian formalism 405
B.2 Hamiltonian formalism 407
C Coherent states of a harmonic oscillator 409
References 412
Index 421 |
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| index_date | 2024-07-02T13:21:46Z |
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| isbn | 0521854210 9780521854214 |
| language | English French |
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| spelling | Dauxois, Thierry 1967- Verfasser (DE-588)124119417 aut Physique des solitons Physics of solitons Thierry Dauxois and Michel Peyrard Engl. ed., 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XII, 422 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physique de l'état solide Solitons Solitons gtt Théories non linéaires Soliton (DE-588)4135213-0 gnd rswk-swf Soliton (DE-588)4135213-0 s DE-604 Peyrard, Michel Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014178974&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dauxois, Thierry 1967- Peyrard, Michel Physics of solitons Physique de l'état solide Solitons Solitons gtt Théories non linéaires Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4135213-0 |
| title | Physics of solitons |
| title_alt | Physique des solitons |
| title_auth | Physics of solitons |
| title_exact_search | Physics of solitons |
| title_exact_search_txtP | Physics of solitons |
| title_full | Physics of solitons Thierry Dauxois and Michel Peyrard |
| title_fullStr | Physics of solitons Thierry Dauxois and Michel Peyrard |
| title_full_unstemmed | Physics of solitons Thierry Dauxois and Michel Peyrard |
| title_short | Physics of solitons |
| title_sort | physics of solitons |
| topic | Physique de l'état solide Solitons Solitons gtt Théories non linéaires Soliton (DE-588)4135213-0 gnd |
| topic_facet | Physique de l'état solide Solitons Théories non linéaires Soliton |
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