Soliton phenomenology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1990
|
| Series: | Mathematics and its applications / Soviet series
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 452 S. |
| ISBN: | 9027728305 |
Staff View
MARC
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| 100 | 1 | |a Machankov, Vladimir G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Soliton phenomenology |c by Vladimir G. Makhankov |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1990 | |
| 300 | |a XI, 452 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics and its applications / Soviet series |v 33 | |
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Record in the Search Index
| _version_ | 1804118499825549312 |
|---|---|
| adam_text | Table of Contents
Series Editor s Preface v
Preface xi
Introduction 1
References 8
PART I. QUANTUM SYSTEMS AND CLASSICAL BEHAVIOUR 13
Chapter 1.
Some physical models and nonlinear differential equations 13
1. Magnetic chain (the Heisenberg model) 13
2. Magnetic chain with magnon phonon interaction 23
3. Nonlinearity of exchange integrals andphonon anharmonism in the Heisenberg model 25
4. Anisotropic magnetic chain in an external field breaking f/(1) (XY) symmetry 28
5. Generalized Hubbard model 30
6. Low frequency wave interaction with a packet ofh.f waves in plasmas 35
7. The j 5 Schrodinger equation as a model to describe collective motions in nuclei 40
8. Colour generalization of a magnetic chain with magnon phonon interaction 42
9. Multicolour Hubbard model 49
Chapter 2.
Physically interesting nonlinear differential equations 55
1. Equations with quadratic dispersion 56
2. Equations with linear dispersion 61
3. Relativistically invariant equations 66
4. Dynamical systems given by differential difference equations 71
References 73
PART II. SOME EXACT RESULTS IN ONE DIMENSIONAL SPACE 81
Chapter 3.
The Nonlinear Schrodinger equation and the Landau Lifshitz equation 87
1. NSE associated with a symmetric space 88
2. The Sigma model representation of the NSE and the isotropic Landau Lifshitz equation 93
3. Gauge connections of the LLE with uniaxial anisotropy and the NSE 106
viii Table of contents
Chapter 4.
Nonlinear Schrodinger equation with U(p,q) internal symmetry and the SG equation 113
1. Equations of motion and the internal symmetry group 113
2. U(p,q) NSE under trivial boundary conditions 117
3. The U(1,O) model . . 121
4. The U(O,1) model 126
5. The U(l,l) model 130
6. Quasi classical quantization of the U(1,J) NSE 135
7. The SG equation 137
References 143
PART III. NONCOMPACT SYMMETRIES AND BOSE GAS 149
Chapter 5.
Dynamical symmetry and generalized coherent states 149
1. Bose gas and dynamical symmetry group 149
2. Quantum version (GCS) 152
3. Quantum version. The representation in the form of a path integral over GCS 166
4. Quantum version. Some concrete models with dynamical symmetry 169
5. Weakly nonideal Bose gas. A classical approach 178
Chapter 6.
Bose gas, integrable NSE and Landau Lifshitz models 183
1. Quantum models and nonlinear classical models corresponding to them.
A new formulation of the reduction procedure 183
2. Nonlinear one dimensional integrable models 187
3. The isotropic Landau Lifshitz SU(1,1) model 189
4. Bose gas models and nonlinear sigma models. Summary 203
5. The third version The sigma model representation connected with
the nonlinear Schrodinger equation 205
6. On the reduction procedure 208
Chapter 7.
£6 theory and Bose drops 211
1. General relations and sohtons drops (particle like solutions) 212
2. Condensate states and their weak excitations 215
3. Localized soliton like excitations of the condensate 218
References 221
Table of Contents ix
PART IV. SOLITON LIKE SOLUTIONS IN ONE DIMENSION 227
Chapter 8.
The class of soliton solutions to the vector version of NSE with self consistent potentials 227
1. Soliton solutions to the U(n) NSE. Linearization method 227
2. U(2) NSE. Dubrovin Krichever technique 231
3. The self consistent conditions 238
4. U(2) NSE. A modification of the Dubrovin Krichever technique 242
5. U(n) system with the Boussinesqpotential 246
Chapter 9.
The existence of soliton like solutions 255
1. Virial relations 255
2. Mechanical analogy method 261
Chapter 10.
Soliton stability 267
1. Stability of hole like excitations in the f 6 model of nonlinear Schrodinger equation.
The spectral analysis 270
2. Stability of drop like solitons. Variational methods 273
3. Structural stability 281
References 283
PART V. PHENOMENOLOGY OF D = 1 SOLITONS 289
Chapter 11.
Dynamics of the formation and interaction of plane solitons 289
1. Computational procedures 290
2. KdV like equations 291
3. NSE like equations 296
4. Equation for induced processes 301
5. Relativistically invariant equations (RIE) 304
6. Bound states of solitons (bions) 306
7. Kink antikink interactions in the J 4 model 309
8. Kink antikink collisions in the MSG model 316
9. Bions in the f 4_ theory 318
10. Small amplitude expansions 320
Chapter 12.
Structural stability and pinning of solitons 323
1. Static bound states 325
2. Bifurcational perturbation theory 328
3. Static states of the long Josephson junction with a single inhomogeneity 334
4. Passing region 339
x Table of contents
Chapter 13.
Dynamical structure factors of soliton gas 345
1. General technique to calculate the dynamical formfactors of solitons 349
2. Dynamic structure factor scattering on a soliton gas.
The SG model: phenomenological approach 352
3. CsNiF3 and the SG model 363
4. The ideal gas phenomenology and the i# 4 model 368
5. Soliton gas kinetics 369
6. Turbulence of a soliton gas 375
References 378
PART VI. MANY DIMENSIONAL SOLITONS 391
Chapter 14.
Existence and stability 391
1. Existence 392
2. Quasi stationary solitons 400
3. Stability of many dimensional stationary solitons 402
4. Static ring shaped fluxons (the structure stability) 409
Chapter 15.
Pulsons and Q solitons 413
1. Collapse of circular and spherical bubbles 413
2. Properties of pulsons 415
3. Pulson stability 418
4. Pulson interaction 420
Chapter 16.
Interaction of Q solitons 429
1. Nonrelativistic models 429
2. Relativistic models 434
3. Formfactors and DSF. 441
References 445
Index 449
|
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| author | Machankov, Vladimir G. |
| author_facet | Machankov, Vladimir G. |
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| author_sort | Machankov, Vladimir G. |
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| 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.BV004310542 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:11:17Z |
| institution | BVB |
| isbn | 9027728305 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002680361 |
| oclc_num | 246570344 |
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| owner_facet | DE-12 DE-739 DE-188 DE-91G DE-BY-TUM |
| physical | XI, 452 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Machankov, Vladimir G. Verfasser aut Soliton phenomenology by Vladimir G. Makhankov Dordrecht u.a. Kluwer Acad. Publ. 1990 XI, 452 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 33 Literaturangaben Soliton (DE-588)4135213-0 gnd rswk-swf Nichtlineares Phänomen (DE-588)4136065-5 gnd rswk-swf Soliton (DE-588)4135213-0 s Nichtlineares Phänomen (DE-588)4136065-5 s DE-604 Soviet series Mathematics and its applications 33 (DE-604)BV004708148 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002680361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Machankov, Vladimir G. Soliton phenomenology Soliton (DE-588)4135213-0 gnd Nichtlineares Phänomen (DE-588)4136065-5 gnd |
| subject_GND | (DE-588)4135213-0 (DE-588)4136065-5 |
| title | Soliton phenomenology |
| title_auth | Soliton phenomenology |
| title_exact_search | Soliton phenomenology |
| title_full | Soliton phenomenology by Vladimir G. Makhankov |
| title_fullStr | Soliton phenomenology by Vladimir G. Makhankov |
| title_full_unstemmed | Soliton phenomenology by Vladimir G. Makhankov |
| title_short | Soliton phenomenology |
| title_sort | soliton phenomenology |
| topic | Soliton (DE-588)4135213-0 gnd Nichtlineares Phänomen (DE-588)4136065-5 gnd |
| topic_facet | Soliton Nichtlineares Phänomen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002680361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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