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

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Ќазвание: Singular limits of dispersive waves

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

јннотаци€:

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.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1994

 оличество страниц: 369

ƒобавлена в каталог: 16.02.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$L - A$ pair      79
$t$-function      70 275 283
Abel hierarchy      84Ч87
Abel transform      78 80 107 177
Abelian differential      3 8 9 16 106Ч108 115 162
Abelian integral      108 109 288
action      166 173 216 241 274 278 305Ч306 311
Adams Ч Bashfort method      333Ч335 337 341
Adiabatic      105 113 216 274
Angle-representation      276 279 281 283Ч288
Asymptotic ansatz      113 114 179
Atomic measure      251Ч253
Attractor      39Ч40 52
Autocorrelation function      183Ч201
Averaged Whitham equation for Toda lattice      5Ч10
Backlund transformation      118 146
Baker vector/Baker function      121 122
Baker Ч Akhiezer function      9 79Ч82 109 112 118 120 177
Benney equations      53 55Ч59 61 65 143Ч155 168 170
Benney hierarchy      61Ч62 65
Bifurcation      39Ч40 48 305 306 309 311
Billiards      219Ч234
Binary oscillation      331Ч332; see Period-two oscillation
Boltzmanfi type equation      220 225 233
Boussinesq equation      61 64Ч65
Branch points of a Riemann surface      3 8 10 11 16 41 56 59 65 70 71 74 76 80 84 106Ч108 110 111 113Ч115 143 179
Breather      40Ч51 283
Brownian motion      233
Bunimovich Ч Sinai theorem      219 220 233
BurgerТs Equation      28 136Ч140 157 160 161 329 330
C. Neumann problem      279 285 286 288
Cantor set      301 304 305 310 311
CauchyТs kernel      65 79Ч82
Caustic      23Ч24 34Ч35 240Ч243 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      357Ч359
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 149Ч153 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      183Ч201
Curvature      144
Cusp / cuspidal      119 126 133 139Ч140
Cuts      62Ч64
CYCLE      42Ч43 71Ч72 75 106 108 216 282
Darboux transformations      117Ч134
Defocusing NLS equation      21Ч27 235Ч238 242Ч245 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      61Ч66
Dispersionless limit of integrable systems      165Ч174
Dispersive hydrodynamics      89Ч104
Divisor      120 122 125 177 179 297 302 304
Doppler frequency      324 325
Dressing      174 177
Driver amplitude      44Ч45
Driver frequency      43
Dubrovin equations      107 114Ч115
Duhamel integral      212
Dyson formula      260
Egorov class      145Ч147
Eikonal equation      22 28 34 35 36 240 241
Einstein Ч Kubo formula      233Ч234
Electrophoresis      144 145 153
Ellipsoid      276 277
Elliptic curve      120 122
Elliptic functions      68 265
Elliptic integrals      68 74 94Ч96 103 135 137 143 160 204 265 267 269
Energy density      316
Energy-phase modulation equations      43Ч44
Entropy solution of Hopf equation      333
Euler hydrodynamics equations      94
Euler system      237 238 254
Euler Ч Poisson type equation      90 96 136Ч139
Evolution equations      37 111
Finite horizon property of a billiard      222Ч223 228 230 233Ч234
Finite-gap      69Ч70 78Ч80 82Ч84 175Ч180 204 205 208 209 211 215 216 289
FlaschkaТs form of Toda lattice equations      6
Focusing NLS equation      27Ч37 235 236 242Ч245 249 283
Fractional power      62
Free energy      316 319
fundamental frequency      300 304
Galilean invariance of NLS      28
Galilei transformations      145Ч147 149 151 153
Gas dynamics      22 169 173
Gas law      22 23
Gauge invariance / gauge transform      168 172
Gauss hypergeometric function      100
Gelfand Ч Dikii Уfractional powerФ ansatz      62
Gelfand Ч Levitan integral equations      177
Generalized hodograph method      89 90Ч94 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      273Ч295
GHM      see Generalized hodograph method
Goursat problem      90 97 101
GP problem      see Gurevich Ч Pitaevsky problem
Grassmanian      118Ч120
GreenТs formula      231
GreenТs function      304
Gurevich Ч Pitaevsky problem      89 90Ч94 96Ч99 203
Hamilton Ч Jacobi equation      63 65 173 174 213
Hamiltonian      61Ч62 105Ч107 112 173 174 183 275Ч280 286 287 289 290 298 299 305
Hamiltonian flow      105 114 276 278 279 285 286 287
Hamiltonian system      68 105 107 143Ч146 150Ч153 167 173 216 236 257 273 278 280 281 285Ч288 298 302
harmonic oscillator      299Ч300
Heat transfer      316
Helix      320 326
Hilbert space      303
Hilbert transform      254 350
Hilbert Ч Schmidt operator      230
Hodograph      4 16 61 63 68Ч69 89 90Ч94 99 102 103 109 136Ч140 154
Holomorphic differential      42 72 73 75 77 106 177
Homoclinic      40 273Ч275 279 285Ч288
Hopf equation      249 329 331 333Ч337 341Ч344 359
Hydrodynamic symmetries      92 149
Hydrodynamic-type equations/systems      53 67 68 89 143 145 149Ч154 225
Hyperelliptic      70Ч78 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      165Ч174
Invariant tori      105 216 276 279 300 302
Inverse scattering problem method      53Ч59 61 135 167 170 176 178 246 248 251 259 348
Inverse scattering transform      67 69 79 81 249
Ising chain      183Ч201
Isospectral symmetries      79Ч82
ISP method      see Inverse scattering problem method
Its Ч Matveev formula      175 204
Jacobi $q$-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 Ч van Moerbeke lattice      331 341 342
Kadomtsev Ч Petviashvili equation      67 69 78Ч84 123 132 167Ч168
Kadomtsev Ч Petviashvili equation, dispersionless      167Ч168
Kadomtsev Ч Petviashvili equation, finite-gap inverse scattering transform for      81
Kadomtsev Ч Petviashvili equation, finite-gap solutions      69 78Ч79 82Ч84
Kadomtsev Ч Petviashvili equation, isospectral symmetries      79Ч82
Kadomtsev Ч Petviashvili equation, Lax pair for      81
Kadomtsev Ч Petviashvili equation, nonisospectral symmetries      82Ч84
KAM theory      see Kolmogorov Ч Arnold Ч Moser theory
KdV equation, see Korteveg Ч de-Vries equation KdV functions      212
KdV hierarchy      84 347Ч356
KdV hydrodynamics      89 91
KdV Ч Whitham problem      2 3
KdV Ч Whitham problem vs. Toda Ч Whitham problem      2
kinetic energy      305 306 310
KN equation      see Krichever Ч Novikov equation
Kolmogorov Ч Arnold Ч Moser theory      114 180 205 302
Kolmogorov Ч Petrovsky Ч Piskunov problem      322
Korteveg Ч de-Vries equation      2 4 53Ч55 61 64 67Ч88 89 90Ч93 95 96 119 126Ч128 131Ч133 143Ч155 157 162 163 175Ч181 203 205Ч209 216 238 248 249 259 275Ч280 284Ч291 298 330 345 347-356
Korteveg Ч de-Vries equation, $L - A$ pair for      79
Korteveg Ч de-Vries equation, $L$-equation for      53 55
Korteveg Ч de-Vries equation, averaged      4 68 70 143Ч155
Korteveg Ч de-Vries equation, dispersionless      4 53Ч55 61 64 180
Korteveg Ч de-Vries equation, finite-gap solutions      69 79Ч80 82Ч84 175Ч180 208 209 216
Korteveg Ч de-Vries equation, isospectral symmetries      79Ч82
Korteveg Ч de-Vries equation, Lax pair for      79
Korteveg Ч de-Vries equation, linearized      206
Korteveg Ч de-Vries equation, moving waves      67
Korteveg Ч de-Vries equation, nonisospectral symmetries of      67Ч88
Korteveg Ч de-Vries equation, quasi-periodic solutions      4
Korteveg Ч de-Vries equation, reflecting coefficient for      54
Korteveg Ч de-Vries equation, shock problem for      176Ч179
Korteveg Ч de-Vries equation, symmetries of      69
Korteveg Ч de-Vries equation, Tsarev equations for      90 162
Korteveg Ч de-Vries equation, wave breaking problem for      89 90Ч93
Korteveg Ч de-Vries equation, weak dispersion limit of      2 4
kp      see Kadomtsev Ч Petviashvili equation
KP flow      117 118 125
KP hierarchy      119
KP vertex operator      130
Krasnoselskii theorem      306
Krichever Ч Novikov equation      119 127 131Ч133
Krichever Ч NovikovТs formalism      120 123
KricheverТs scheme      109
Kruskal symmetries      149 150 152
Kuzmak Ч Whitham averaging ansatz      105 114
Lagrangian      173
Lagrangian submanifold      278 280 281 286 289
Laminar state      315 316
Laplace integral      261
Laplace Ч Beltrami type operator      290
Lax entropy      237
Lax equations      61Ч66 167
Lax equivalence theorem      227 233
Lax pairr      6 79 81 257
Lax Ч Levermore minimizer      157Ч164
Lax Ч Levermore problem      203
Lax Ч Levermore Ч Venakides theory      14 135 162
Legendre transform      305
Lie algebras      289
Lie derivative      77
Line bundle      118 120Ч122 126
Linear fractional transformation      123 127
Linear stability      318Ч319
Liouville equation      233Ч234
Liouville theorem      186
Liouville tori      105Ч116
Lorentz gas of hard spheres      219Ч227 229Ч230
Lorentz gas with accomodation reflection      221Ч223 227Ч228 230-233
Lyapounov functional      316
Lyapounov theorem      316
Lyapounov Ч Schmidt decomposition      302 304Ч305
Magnetic field      183Ч201
Markov partition      219 233
Maslov method      289
Modulation equations      27Ч28 37 39Ч52 89 331 333 342 345
Moduli space      76 78 273
monodromy      273Ч295
Moving frame      258
Multi-phase averaged system      135 143 149
Multifrequency averaging theory      203Ч217
Multiphase asymptotics      204 215
Nash Ч 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      21Ч38 55 61 93Ч95 169 180 235Ч255 276 279Ч281 283 291 298 328
Non-linear Schr$\ddot{o}$dinger equation, defocusing      21Ч27 89 93Ч94 235Ч238 242Ч245 248 249 251 276 279 283
Non-linear Schr$\ddot{o}$dinger equation, focusing      27Ч37 235 236 242Ч245 249 283
Non-linear Schr$\ddot{o}$dinger equation, Galilean invariance of      28
Non-linear Schr$\ddot{o}$dinger equation, semiclassical theory of      21Ч37 235Ч255
Non-linear waves      297Ч313
Nondissipative shock waves      89Ч92 97 98 99 102
Nonisospectral integrable equations      69
Nonisospectral symmetries      78Ч79 82Ч87
Nonlinear wave equation      299 303 305
NSW      see Nondissipative shock waves
Number density      220Ч221 223Ч225 228 233
Numerical scheme      329 342
Optical fibers      24Ч27
Optical pulses      24
Optical shocks      21Ч37
Oscillations arising in numerical experiments      329Ч346
Painleve equation      105
Parabolic structure      121 122
Pauli matrices      183
Period matrix      41Ч43 78
Period-two oscillations      331Ч333 336Ч345
Periodic solutions      297 299 300Ч302 304 307 310
Perturbed modulation equations, numerical integration of      44Ч51
Phase space      220 276 279 280 297 302
Poisson bracket      62 144 174 236 247
Potential      80 81 90 94Ч96 105 107 112 150 177 179 211 235 236 240 299 305Ч307 311
Potential metric      146 151Ч153
Pre-chaotic      40 52
Presoliton solutions      291
Principle of least action      305Ч306 311 312
Quadric      274 276 288
Quasi-periodic geodesic      277 279
Quasi-periodic solutions      286 291 297
Quasi-simple wave      89 90 92 99Ч103 367
Quasiclassical limit      53Ч59 207
Quasimomentum      72 80 211
Reflection laws      219Ч222 234
Regularization of integrals      53 57
Resonance      105 203Ч217 297Ч313
Resonant group      300Ч302 304
Reynolds number      315
RH problem      see Riemann Ч Hilbert problem
Riccati equation      54 124
Riemann (diagonal, characteristic) form      68 84 89 254
Riemann bilinear relations      72Ч74 268
Riemann constants      78 81
Riemann invariant form of      61
Riemann invariants      22 62 68Ч70 92 143 238 239 249 255
Riemann manifold      290
Riemann metric      290
Riemann problem      75Ч78
Riemann surface      3 8 10 11 16 41Ч43 56 59 65 70Ч78 80 81 112 143 146 216 254 269 274 276 280 282Ч284 286 287 289
Riemann surface, branch points of      3 8 10 11 16 41 56 59 65 70 71 74 76 80 106Ч108 110 111 143
Riemann surface, cycles on      42Ч43 71Ч72 106 108 282
Riemann surface, deformations of      75Ч78
Riemann surface, differentials on      71Ч75 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      75Ч78
Riemann theta function      41 78 106 112 113 118 204 211
Riemann wave      92 99
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