Ercolani N.M., Gabitov I.R., Levermore C.D. — Singular limits of dispersive waves :: Электронная библиотека попечительского совета мехмата МГУ

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Ercolani N.M., Gabitov I.R., Levermore C.D. — Singular limits of dispersive waves

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Название: Singular limits of dispersive waves

Авторы: Ercolani N.M., Gabitov I.R., Levermore C.D.

Аннотация:

In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, and forced by gravity and surface tension. As a result, water with a free surface is generally considered to be a dispersive medium.
Surface gravity waves, moving under the forcing by gravity, propagate faster for increasing wavelength. For a given wavelength, gravity waves in deeper water have a larger phase speed than in shallower water. In contrast with this, capillary waves only forced by surface tension, propagate faster for shorter wavelengths.
Besides frequency dispersion, water waves also exhibit amplitude dispersion. This is a nonlinear effect, by which waves of larger amplitude have a different phase speed from small-amplitude waves.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 369

Добавлена в каталог: 16.02.2014

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Предметный указатель

pair      79
-function      70 275 283
Abel hierarchy      84—87
Abel transform      78 80 107 177
Abelian differential      3 8 9 16 106—108 115 162
Abelian integral      108 109 288
action      166 173 216 241 274 278 305—306 311
Adams — Bashfort method      333—335 337 341
Adiabatic      105 113 216 274
Angle-representation      276 279 281 283—288
Asymptotic ansatz      113 114 179
Atomic measure      251—253
Attractor      39—40 52
Autocorrelation function      183—201
Averaged Whitham equation for Toda lattice      5—10
Backlund transformation      118 146
Baker vector/Baker function      121 122
Baker — Akhiezer function      9 79—82 109 112 118 120 177
Benney equations      53 55—59 61 65 143—155 168 170
Benney hierarchy      61—62 65
Bifurcation      39—40 48 305 306 309 311
Billiards      219—234
Binary oscillation      331—332; see Period-two oscillation
Boltzmanfi type equation      220 225 233
Boussinesq equation      61 64—65
Branch points of a Riemann surface      3 8 10 11 16 41 56 59 65 70 71 74 76 80 84 106—108 110 111 113—115 143 179
Breather      40—51 283
Brownian motion      233
Bunimovich — Sinai theorem      219 220 233
Burger’s Equation      28 136—140 157 160 161 329 330
C. Neumann problem      279 285 286 288
Cantor set      301 304 305 310 311
Cauchy’s kernel      65 79—82
Caustic      23—24 34—35 240—243 279
Central limit theorem      233
Chaos / chaotic      40 105 331 336 339 342
Characteristic speed/velocity      4 5 14 15 64
Christophel symbols      144
Chromatography      144 145 153
Compatibility conditions in shock dynamics      357—359
Complex structure, deformation of      70 73 77 78
Complex tori      75
Configuration space      205
Conformal field theory      70
Connection      77 274 283
Conoidal waves      203 255
Conservation laws      5ff 37 68 90 94 145 146 149—153 236 240 330 331 332 345 357 360
Contact discontinuity      329 333 336 341 342 345
Contraction principle      351
Contravariant derivative      290
Convection      315 316
Couette flow      315 316
Covariant derivative      290
Critical magnetic field      183—201
Curvature      144
Cusp / cuspidal      119 126 133 139—140
Cuts      62—64
CYCLE      42—43 71—72 75 106 108 216 282
Darboux transformations      117—134
Defocusing NLS equation      21—27 235—238 242—245 248 249 251 276 279 283
Degree of mapping Z      1
Diffusion coefficient      219 220 226 228 233 234
Diffusion equation      219 226 228
Dirac operator      246
Dispersionless Lax equations      61—66
Dispersionless limit of integrable systems      165—174
Dispersive hydrodynamics      89—104
Divisor      120 122 125 177 179 297 302 304
Doppler frequency      324 325
Dressing      174 177
Driver amplitude      44—45
Driver frequency      43
Dubrovin equations      107 114—115
Duhamel integral      212
Dyson formula      260
Egorov class      145—147
Eikonal equation      22 28 34 35 36 240 241
Einstein — Kubo formula      233—234
Electrophoresis      144 145 153
Ellipsoid      276 277
Elliptic curve      120 122
Elliptic functions      68 265
Elliptic integrals      68 74 94—96 103 135 137 143 160 204 265 267 269
Energy density      316
Energy-phase modulation equations      43—44
Entropy solution of Hopf equation      333
Euler hydrodynamics equations      94
Euler system      237 238 254
Euler — Poisson type equation      90 96 136—139
Evolution equations      37 111
Finite horizon property of a billiard      222—223 228 230 233—234
Finite-gap      69—70 78—80 82—84 175—180 204 205 208 209 211 215 216 289
Flaschka’s form of Toda lattice equations      6
Focusing NLS equation      27—37 235 236 242—245 249 283
Fractional power      62
Free energy      316 319
fundamental frequency      300 304
Galilean invariance of NLS      28
Galilei transformations      145—147 149 151 153
Gas dynamics      22 169 173
Gas law      22 23
Gauge invariance / gauge transform      168 172
Gauss hypergeometric function      100
Gelfand — Dikii “fractional power” ansatz      62
Gelfand — Levitan integral equations      177
Generalized hodograph method      89 90—94 99 109 154
Genus      2 4 5 8 13 16 17 70 71 75 81 106 118 175 254 267 269
Geodesic flow, ergodic property of      219
Geometric phases      273—295
GHM      see Generalized hodograph method
Goursat problem      90 97 101
GP problem      see Gurevich — Pitaevsky problem
Grassmanian      118—120
Green’s formula      231
Green’s function      304
Gurevich — Pitaevsky problem      89 90—94 96—99 203
Hamilton — Jacobi equation      63 65 173 174 213
Hamiltonian      61—62 105—107 112 173 174 183 275—280 286 287 289 290 298 299 305
Hamiltonian flow      105 114 276 278 279 285 286 287
Hamiltonian system      68 105 107 143—146 150—153 167 173 216 236 257 273 278 280 281 285—288 298 302
harmonic oscillator      299—300
Heat transfer      316
Helix      320 326
Hilbert space      303
Hilbert transform      254 350
Hilbert — Schmidt operator      230
Hodograph      4 16 61 63 68—69 89 90—94 99 102 103 109 136—140 154
Holomorphic differential      42 72 73 75 77 106 177
Homoclinic      40 273—275 279 285—288
Hopf equation      249 329 331 333—337 341—344 359
Hydrodynamic symmetries      92 149
Hydrodynamic-type equations/systems      53 67 68 89 143 145 149—154 225
Hyperelliptic      70—78 80 106 126 175 204 209 211 215 276
Hypergeometric equation      99
Hypergeometric function      100
Integrable / nonintegrable numerical scheme      329 331 336 341 342 345
Integrable system      165—174
Invariant tori      105 216 276 279 300 302
Inverse scattering problem method      53—59 61 135 167 170 176 178 246 248 251 259 348
Inverse scattering transform      67 69 79 81 249
Ising chain      183—201
Isospectral symmetries      79—82
ISP method      see Inverse scattering problem method
Its — Matveev formula      175 204
Jacobi -function      204
Jacobi identity      144
Jacobi problem      286 288
Jacobi transformation      267
Jacobi variety      273 274 279 281 283 286 289
Jacobian      106

Jacobian matrix      332
Jost functions      54
Kac — van Moerbeke lattice      331 341 342
Kadomtsev — Petviashvili equation      67 69 78—84 123 132 167—168
Kadomtsev — Petviashvili equation, dispersionless      167—168
Kadomtsev — Petviashvili equation, finite-gap inverse scattering transform for      81
Kadomtsev — Petviashvili equation, finite-gap solutions      69 78—79 82—84
Kadomtsev — Petviashvili equation, isospectral symmetries      79—82
Kadomtsev — Petviashvili equation, Lax pair for      81
Kadomtsev — Petviashvili equation, nonisospectral symmetries      82—84
KAM theory      see Kolmogorov — Arnold — Moser theory
KdV equation, see Korteveg — de-Vries equation KdV functions      212
KdV hierarchy      84 347—356
KdV hydrodynamics      89 91
KdV — Whitham problem      2 3
KdV — Whitham problem vs. Toda — Whitham problem      2
kinetic energy      305 306 310
KN equation      see Krichever — Novikov equation
Kolmogorov — Arnold — Moser theory      114 180 205 302
Kolmogorov — Petrovsky — Piskunov problem      322
Korteveg — de-Vries equation      2 4 53—55 61 64 67—88 89 90—93 95 96 119 126—128 131—133 143—155 157 162 163 175—181 203 205—209 216 238 248 249 259 275—280 284—291 298 330 345 347-356
Korteveg — de-Vries equation, pair for      79
Korteveg — de-Vries equation, -equation for      53 55
Korteveg — de-Vries equation, averaged      4 68 70 143—155
Korteveg — de-Vries equation, dispersionless      4 53—55 61 64 180
Korteveg — de-Vries equation, finite-gap solutions      69 79—80 82—84 175—180 208 209 216
Korteveg — de-Vries equation, isospectral symmetries      79—82
Korteveg — de-Vries equation, Lax pair for      79
Korteveg — de-Vries equation, linearized      206
Korteveg — de-Vries equation, moving waves      67
Korteveg — de-Vries equation, nonisospectral symmetries of      67—88
Korteveg — de-Vries equation, quasi-periodic solutions      4
Korteveg — de-Vries equation, reflecting coefficient for      54
Korteveg — de-Vries equation, shock problem for      176—179
Korteveg — de-Vries equation, symmetries of      69
Korteveg — de-Vries equation, Tsarev equations for      90 162
Korteveg — de-Vries equation, wave breaking problem for      89 90—93
Korteveg — de-Vries equation, weak dispersion limit of      2 4
kp      see Kadomtsev — Petviashvili equation
KP flow      117 118 125
KP hierarchy      119
KP vertex operator      130
Krasnoselskii theorem      306
Krichever — Novikov equation      119 127 131—133
Krichever — Novikov’s formalism      120 123
Krichever’s scheme      109
Kruskal symmetries      149 150 152
Kuzmak — Whitham averaging ansatz      105 114
Lagrangian      173
Lagrangian submanifold      278 280 281 286 289
Laminar state      315 316
Laplace integral      261
Laplace — Beltrami type operator      290
Lax entropy      237
Lax equations      61—66 167
Lax equivalence theorem      227 233
Lax pairr      6 79 81 257
Lax — Levermore minimizer      157—164
Lax — Levermore problem      203
Lax — Levermore — Venakides theory      14 135 162
Legendre transform      305
Lie algebras      289
Lie derivative      77
Line bundle      118 120—122 126
Linear fractional transformation      123 127
Linear stability      318—319
Liouville equation      233—234
Liouville theorem      186
Liouville tori      105—116
Lorentz gas of hard spheres      219—227 229—230
Lorentz gas with accomodation reflection      221—223 227—228 230-233
Lyapounov functional      316
Lyapounov theorem      316
Lyapounov — Schmidt decomposition      302 304—305
Magnetic field      183—201
Markov partition      219 233
Maslov method      289
Modulation equations      27—28 37 39—52 89 331 333 342 345
Moduli space      76 78 273
monodromy      273—295
Moving frame      258
Multi-phase averaged system      135 143 149
Multifrequency averaging theory      203—217
Multiphase asymptotics      204 215
Nash — Moser method      297 302 304
Neumann system      105 111 112 114
NLS equation      see non-linear Schr $\ddot{o}$ dinger equation
Non-linear Schr $\ddot{o}$ dinger equation      21—38 55 61 93—95 169 180 235—255 276 279—281 283 291 298 328
Non-linear Schr $\ddot{o}$ dinger equation, defocusing      21—27 89 93—94 235—238 242—245 248 249 251 276 279 283
Non-linear Schr $\ddot{o}$ dinger equation, focusing      27—37 235 236 242—245 249 283
Non-linear Schr $\ddot{o}$ dinger equation, Galilean invariance of      28
Non-linear Schr $\ddot{o}$ dinger equation, semiclassical theory of      21—37 235—255
Non-linear waves      297—313
Nondissipative shock waves      89—92 97 98 99 102
Nonisospectral integrable equations      69
Nonisospectral symmetries      78—79 82—87
Nonlinear wave equation      299 303 305
NSW      see Nondissipative shock waves
Number density      220—221 223—225 228 233
Numerical scheme      329 342
Optical fibers      24—27
Optical pulses      24
Optical shocks      21—37
Oscillations arising in numerical experiments      329—346
Painleve equation      105
Parabolic structure      121 122
Pauli matrices      183
Period matrix      41—43 78
Period-two oscillations      331—333 336—345
Periodic solutions      297 299 300—302 304 307 310
Perturbed modulation equations, numerical integration of      44—51
Phase space      220 276 279 280 297 302
Poisson bracket      62 144 174 236 247
Potential      80 81 90 94—96 105 107 112 150 177 179 211 235 236 240 299 305—307 311
Potential metric      146 151—153
Pre-chaotic      40 52
Presoliton solutions      291
Principle of least action      305—306 311 312
Quadric      274 276 288
Quasi-periodic geodesic      277 279
Quasi-periodic solutions      286 291 297
Quasi-simple wave      89 90 92 99—103 367
Quasiclassical limit      53—59 207
Quasimomentum      72 80 211
Reflection laws      219—222 234
Regularization of integrals      53 57
Resonance      105 203—217 297—313
Resonant group      300—302 304
Reynolds number      315
RH problem      see Riemann — Hilbert problem
Riccati equation      54 124
Riemann (diagonal, characteristic) form      68 84 89 254
Riemann bilinear relations      72—74 268
Riemann constants      78 81
Riemann invariant form of      61
Riemann invariants      22 62 68—70 92 143 238 239 249 255
Riemann manifold      290
Riemann metric      290
Riemann problem      75—78
Riemann surface      3 8 10 11 16 41—43 56 59 65 70—78 80 81 112 143 146 216 254 269 274 276 280 282—284 286 287 289
Riemann surface, branch points of      3 8 10 11 16 41 56 59 65 70 71 74 76 80 106—108 110 111 143
Riemann surface, cycles on      42—43 71—72 106 108 282
Riemann surface, deformations of      75—78
Riemann surface, differentials on      71—75 106
Riemann surface, genus of      70 71 75 81 106 254 269
Riemann surface, local parameter      71
Riemann surface, matrix of periods      78
Riemann surface, moduli space of      75—78
Riemann theta function      41 78 106 112 113 118 204 211
Riemann wave      92 99

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