Waves Called Solitons: Concepts and ExperimentsIn the third edition the presentation of new topics has been deliberately kept simple for pedagogical purposes. Chapter 1 was completed by references to the tidal bore and magnetic envelope solitons. Two new sections devoted to magnetic envelope solitons and signal processing with solitons have been added to Chap. 4. Short comments on models describing blood-pressure pulse propagation in terms of solitons were added to chapter 5. A description of a new mechanical transmission line with two equilibrium states has been included in Chap. 6. Such an analog device is useful to illustrate the properties of kink-solitons and to observe solitary waves with a compact shape, called compactons. New references conceming recent advances in experimental techniques and lattice effects were added to Chap. 7. In Chap. 8 a short introduction to spatial optical solitons in continuous and discrete systems was included. Chapter 9 was completed by new sections devoted to nonlinear lattice models and energy localization. The concepts of self-trapped states and intrinsic localized modes or discrete breathers are dicussed. Different analog chains which make it possible to observe the characteristic features of discrete breathers, are described. Contrary to previous chapters where we have considered reversible or conservative systems where solitons can exist owing to the dynamical balance between linear dispersion and nonlinearity, Chapter 11 which is a new chapter, is devoted to irreversible systems where nonlinearity can balance the effects of dissipation leading to "diffusing solitary waves" or "diffusive solitons". |
Contents
I | 3 |
II | 5 |
III | 9 |
IV | 13 |
V | 14 |
VII | 17 |
VIII | 20 |
IX | 21 |
XCVIII | 169 |
XCIX | 172 |
C | 173 |
CI | 175 |
CII | 177 |
CIII | 180 |
CIV | 181 |
CV | 182 |
X | 23 |
XI | 25 |
XII | 28 |
XIII | 29 |
XIV | 33 |
XV | 36 |
XVI | 39 |
XVII | 43 |
XVIII | 44 |
XIX | 48 |
XX | 50 |
XXI | 54 |
XXII | 58 |
XXIII | 60 |
XXIV | 62 |
XXV | 64 |
XXVI | 66 |
XXVII | 67 |
XXVIII | 69 |
XXIX | 70 |
XXX | 72 |
XXXI | 73 |
XXXII | 74 |
XXXIII | 76 |
XXXIV | 78 |
XXXV | 79 |
XXXVI | 84 |
XXXVII | 86 |
XXXVIII | 88 |
XXXIX | 90 |
XLII | 91 |
XLIII | 93 |
XLV | 95 |
XLVI | 97 |
XLVII | 98 |
XLVIII | 100 |
XLIX | 105 |
LI | 106 |
LII | 107 |
LIII | 110 |
LV | 111 |
LVI | 112 |
LVII | 114 |
LVIII | 117 |
LX | 118 |
LXII | 122 |
LXIV | 123 |
LXV | 124 |
LXVI | 125 |
LXVII | 127 |
LXVIII | 128 |
LXX | 129 |
LXXI | 131 |
LXXII | 132 |
LXXIV | 133 |
LXXV | 134 |
LXXVI | 136 |
LXXVII | 137 |
LXXVIII | 138 |
LXXIX | 141 |
LXXX | 145 |
LXXXII | 147 |
LXXXIV | 148 |
LXXXV | 149 |
LXXXVI | 151 |
LXXXVII | 153 |
LXXXVIII | 154 |
LXXXIX | 156 |
XC | 158 |
XCI | 159 |
XCII | 161 |
XCIII | 163 |
XCIV | 165 |
XCVI | 167 |
XCVII | 168 |
CVI | 184 |
CVII | 186 |
CVIII | 187 |
CIX | 189 |
CXI | 191 |
CXIII | 192 |
CXIV | 194 |
CXV | 198 |
CXVI | 200 |
CXVII | 201 |
CXVIII | 203 |
CXX | 205 |
CXXI | 206 |
CXXII | 208 |
CXXIII | 209 |
CXXIV | 210 |
CXXV | 212 |
CXXVI | 213 |
CXXVII | 215 |
CXXVIII | 216 |
CXXIX | 218 |
CXXX | 219 |
CXXXI | 220 |
CXXXII | 221 |
CXXXIII | 223 |
CXXXIV | 224 |
CXXXV | 227 |
CXXXVII | 232 |
CXXXVIII | 234 |
CXXXIX | 235 |
CXL | 237 |
CXLI | 240 |
CXLII | 241 |
CXLIII | 244 |
CXLIV | 246 |
CXLV | 249 |
CXLVI | 252 |
CXLVII | 253 |
CXLVIII | 255 |
CL | 256 |
CLI | 258 |
CLII | 259 |
CLIII | 261 |
CLIV | 262 |
CLV | 264 |
CLVI | 265 |
CLVII | 266 |
CLVIII | 268 |
CLIX | 269 |
CLX | 271 |
CLXI | 272 |
CLXII | 273 |
CLXIII | 275 |
CLXIV | 276 |
CLXV | 277 |
CLXVI | 279 |
CLXVII | 282 |
CLXVIII | 286 |
CLXIX | 287 |
CLXXI | 289 |
CLXXII | 290 |
CLXXIII | 292 |
CLXXIV | 293 |
CLXXV | 295 |
CLXXVI | 298 |
CLXXVII | 300 |
CLXXVIII | 301 |
CLXXIX | 302 |
CLXXX | 303 |
CLXXXII | 304 |
CLXXXIII | 305 |
309 | |
327 | |
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Common terms and phrases
antikink Appendix arctan calculated capacitance carrier wave chain coefficient collision compacton consider constant continuum approximation corresponds coupling described diffusive soliton discrete breathers dispersion relation displacement dissipative effects dynamics electrical network electrical transmission line energy envelope solitons evolution experimental experiments fluid fluxon Fourier frequency function group velocity initial input integration interaction Josephson junction KdV equation kink soliton linear dispersion linear waves localized modes magnetic mechanical modulational instability NLS equation nonlinear dispersion nonlinear Schrödinger equation nonlinear transmission lines nonlinear waves observed obtain optical fibers oscillations parameter particle pendulum perturbation phase velocity Phys physical potential pulse quantum sech Sect Sine-Gordon equation sinusoidal sketched solitary wave soliton solution spatial spin waves superconductors surface tanh Toda lattice transform V₁ variables voltage water waves wave number wave packet wave propagation waveform wavelength wavenumber wavetrain width yields zero ду дх