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Tables of Contents for Nonlinear Science at the Dawn of the 21st Century
Chapter/Section Title
Page #
Page Count
I Nonlinear Science
1
66
Nonlinear Coherent Phenomena in Continuous Media
3
44
E.A. Kuznetsov
V.E. Zakharov
Introduction
3
1
Phase randomization in nonlinear media
4
5
Nonlinear Schrodinger equation
9
2
Solitons in the focusing NSLE
11
4
Collapses in the NLSE
15
3
Weak, strong and superstrong collapses
18
3
Anisotropic black holes
21
5
Structure in media with weak dispersion
26
6
Singularities on a fluid surface
32
2
Solitons and collapses in the generalized KP equation
34
4
Self-focusing in the boundary layer
38
4
References
42
5
Perturbation Theories for Nonlinear Waves
47
20
L. Ostrovsky
K. Gorshkov
Introduction
47
2
Modulated waves
49
2
Direct perturbation method
51
1
Perturbation theories for solitary waves
52
8
Direct perturbation method for solitons: quasistationary approach
52
2
Nonstationary approach
54
1
Inverse-scattering perturbation scheme
55
2
``Equivalence principle''
57
1
Example: soliton interaction in Lagrangian systems
58
1
Radiation from solitons
59
1
Asymptotic reduction of nonlinear wave equations
60
1
Conclusions
61
1
References
62
5
II Superconductivity and Magnetism
67
104
Josephson Devices
69
18
A. Barone
S. Pagano
Introduction
69
1
Elements of the Josephson effect
70
2
SQUIDs
72
3
Digital devices
75
2
Detectors
77
1
Voltage standard
78
2
Microwave oscillators
80
3
Conclusions
83
1
References
83
4
Josephson Flux-Flow Oscillators in Microwave Fields
87
16
M. Salerno
M. Samuelsen
Introduction
87
1
Flux-flow oscillators in uniform microwave fields
88
3
Flux-flow oscillators in non-uniform microwave fields
91
3
Numerical experiment
94
4
Conclusions
98
1
Appendix
98
2
References
100
3
Coupled Structures of Long Josephson Junctions
103
18
G. Carapella
G. Costabile
Stacks of two long Josephson junctions
103
6
The physical system and its model
103
3
Experiments on stacks of two long Josephson junctions
106
3
Parallel arrays of Josephson junctions
109
4
The physical system and its model
109
3
Numerical and experimental results on five-junctions parallel arrays
112
1
Triangular cells of long Josephson junctions
113
5
The model
114
1
Numerical and experimental results
115
3
References
118
3
Stacked Josephson Junctions
121
16
N.F. Pedersen
Introduction
121
1
Short summary of fluxon properties
121
2
Stacked junctions
123
2
Fluxon solutions, selected examples
125
3
The coherent 2-fluxon mode
125
2
The two modes of the two fluxon case
127
1
Stacked junction plasma oscillation solutions
128
7
Conclusion
135
1
References
135
2
Dynamics of Vortices in Two-Dimensional Magnets
137
34
F.G. Mertens
A.R. Bishop
Introduction
137
4
Collective variable theories at zero temperature
141
14
Thiele equation
141
2
Vortex mass
143
3
Hierarchy of equations of motion
146
6
An alternative approach: coupling to magnons
152
3
Effects of thermal noise on vortex dynamics
155
8
Equilibrium and non-equilibrium situations
155
1
Collective variable theory and Langevin dynamics simulations
155
6
Noise-induced transitions between opposite polarizations
161
2
Dynamics above the Kosterlitz-Thouless transition
163
3
Vortex-gas approach
163
1
Comparison with simulations and experiments
164
1
Vortex motion in Monte Carlo simulations
165
1
Conclusion
166
1
References
167
4
III Nonlinear Optics
171
92
Spatial Optical Solitons
173
22
Yu. S. Kivshar
Introduction
173
2
Spatial vs. temporal solitons
175
1
Basic equations
176
2
Stability of solitary waves
178
4
One-parameter solitary waves
179
1
Two-parameter solitary waves
180
2
Experiments on self-focusing
182
2
Soliton spiralling
184
2
Multi-hump solitons and solitonic gluons
186
3
Discrete spatial optical solitons
189
2
References
191
4
Nonlinear Fiber Optics
195
18
G.P. Agrawal
Introduction
195
1
Fiber characteristics
196
2
Single-mode fibers
196
1
Fiber nonlinearities
196
1
Group-velocity dispersion
197
1
Pulse propagation in fibers
198
1
Nonlinear Schrodinger equation
198
1
Modulation instability
198
1
Optical solitons
199
6
Bright solitons
200
1
Dark solitons
201
1
Loss-managed solitons
202
1
Dispersion-managed solitons
203
2
Nonlinear optical switching
205
4
SPM-based optical switching
205
2
XPM-based optical switching
207
2
Concluding remarks
209
1
References
209
4
Self-Focusing and Collapse of Light Beams in Nonlinear Dispersive Media
213
16
L. Berge
J. Juul Rasmussen
Introduction
213
1
General properties of self-focusing with anomalous group velocity dispersion
214
6
Basic properties
214
2
Self-similar wave collapses
216
4
Self-focusing with normal group velocity dispersion
220
4
Discussion of the general properties, outlook
224
2
References
226
3
Coherent Structures in Dissipative Nonlinear Optical Systems
229
18
J.V. Moloney
Introduction
229
5
Nonlinear waveguide channeling in air
234
5
Dynamic spatial replenishment of femtosecond pulses propagating in air
236
3
Control of optical turbulence in semiconductor lasers
239
4
The control
240
3
Summary and conclusions
243
2
References
245
2
Solitons in Optical Media with Quadratic Nonlinearity
247
16
B.A. Malomed
Introduction
247
2
The basic theoretical models
249
4
The solitons
253
7
Conclusion
260
1
References
261
2
IV Lattice Dynamics and Applications
263
108
Nonlinear Models for the Dynamics of Topological Defects in Solids
265
28
Yu.S. Kivshar
H. Benner
O.M. Braun
Introduction
265
1
The FK model and the SG equation
266
3
Physical models
269
8
Dislocations in solids
269
1
Magnetic chains
270
1
Josephson junctions
271
2
Hydrogen-bonded chains
273
2
Surface physics and adsorbed atomic layers
275
1
Models of the DNA dynamics
276
1
Properties of kinks
277
4
On-site potential of general form
277
2
Discreteness effects
279
1
Kinks in external fields
280
1
Compacton kinks
281
1
Experimental verifications
281
4
Josephson junctions
281
2
Magnetic systems
283
2
Concluding remarks
285
1
References
286
7
2-D Breathers and Applications
293
14
J.L. Marin
J.C. Eilbeck
F.M. Russell
Introduction
293
1
Deciphering the lines in mica
294
2
Numerical and analogue studies
296
3
Longitudinal moving breathers in 2D lattices
299
3
Breather collisions
302
1
Conclusions and further applications
303
1
Application to sputtering
303
1
Application to layered HTSC materials
303
1
References
304
3
Scale Competition in Nonlinear Schrodinger Models
307
16
Yu. B. Gaididei
P.L. Christiansen
S.F. Mingaleev
Introduction
307
1
Excitations in nonlinear Kronig-Penney models
308
3
Discrete NLS models with long-range dispersive interactions
311
5
Stabilization of nonlinear excitations by disorder
316
3
Summary
319
1
References
320
3
Demonstration Systems for Kink-Solitons
323
16
M. Remoissenet
Introduction
323
2
Mechanical chains with double-well potential
325
6
Chain with torsion and gravity
325
4
Chain with flexion and gravity
329
1
Numerical simulations
330
1
Experiments
331
2
Chain with torsion and gravity
331
1
Chain with flexion and gravity
332
1
Lattice effects
333
1
Conclusion
334
1
Appendix
335
1
References
336
3
Quantum Lattice Solitons
339
18
A. C. Scott
Introduction
339
1
Local modes in the dihalomethanes
339
5
Classical analysis
340
1
Quantum analysis
341
3
Comparison with experiments
344
1
A lattice nonlinear Schrodinger equation
344
4
Local modes in crystalline acetanilide
348
6
Conclusions
354
1
References
355
2
Noise in Molecular Systems
357
14
G.P. Tsironis
Introduction
357
1
Additive correlated ratchets
358
5
Current reversal
363
1
Synthetic motor protein motion
364
4
Targeted energy transfer and nonequilibrium fluctuations in bioenergetics
368
1
References
369
2
V Biomolecular Dynamics and Biology
371
76
Nonlinear Dynamics of DNA
373
20
L. V. Yakushevich
Introduction
373
2
General description of DNA dynamics. Classification of the internal motions
375
1
Mathematical modeling of DNA dynamics. Hierarchy of the models
376
3
Principles of modeling
376
1
Structural hierarchy
376
1
Dynamical hierarchy
377
2
Nonlinear mathematical models. Solved and unsolved problems
379
2
Ideal models
379
1
Nonideal models
380
1
Statistics of solitons in DNA
380
1
Nonlinear DNA models and experiment
381
4
Hydrogen-tritium (or hydrogen-deuterium) exchange
381
1
Resonant microwave absorption
382
1
Scattering of neutrons and light
383
1
Fluorescence depolarization
384
1
Nonlinear conception and mechanisms of DNA functioning
385
2
Nonlinear mechanism of conformational transitions
385
1
Nonlinear conformational waves and long-range effects
385
1
Direction of transcription process
386
1
References
387
6
From the FPU Chain to Biomolecular Dynamics
393
16
A.V. Zolotaryuk
A.V. Savin
P.L. Christiansen
Introduction
393
1
Helices in two and three dimensions
394
3
Equations of motion for a helix backbone
397
1
Small-amplitude limit
398
2
Three-component soliton solutions
400
5
3D case: solitons of longitudinal compression
402
2
2D case: other types of solutions
404
1
Conclusions
405
2
References
407
2
Mutual Dynamics of Swimming Microorganisms and Their Fluid Habitat
409
18
J.O. Kessler
G.D. Burnett
K.E. Remick
Introduction
409
2
Bioconvection (I)
411
4
Observations
411
1
Continuum theory
412
3
Bacteria in constraining environments (II)
415
2
Possibilities for computer simulation
417
4
Conclusion
421
2
Appendix I: Statistical methods
423
1
Appendix II
424
1
References
425
2
Nonlinearities in Biology: The Brain as an Example
427
20
H. Haken
Introduction
427
1
Some salient features of neurons
427
2
The noisy lighthouse model of a neural network
429
1
The special case of two neurons
430
3
Time-averages
433
1
The averaged neural equations
434
6
How to make contact with experimental data? Synergetics as a guide
440
3
Concluding remarks and outlook
443
1
References
444
3
Index
447