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Debnath L. Ч Nonlinear water waves
Debnath L. Ч Nonlinear water waves

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Ќазвание: Nonlinear water waves

јвтор: Debnath L.

јннотаци€:

Wave motion in water is one of the most striking observable phenomena in nature. Throughout the twentieth century, development of the linearized theory of wave motion in fluids and hydrodynamic stability has been steady and significant. In the last three decades there have been remarkable developments in nonlinear dispersive waves in general, nonlinear water waves in particular, and nonlinear instability phenomena. New solutions are now available for waves modulatedin both space and time, which exhibit new phenomena as diverse as solitons, resonant interactions, side-band instability, and wave-breaking. Other achievements include the discovery of soliton interactions, and the Inverse Scattering Transform method forfinding the explicit exact solution for several canonical nonlinear partial differential equations.
This monograph is the first to summarize the research on nonlinear wave phenomena over the past three decades, and it also presents numerous applications in physics, geophysics, and engineering.


язык: en

–убрика: ‘изика/ олебани€ и волны/

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

ed2k: ed2k stats

√од издани€: 1994

 оличество страниц: 544

ƒобавлена в каталог: 16.08.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel integral equation      297
Ablowitz      193 361 362 363
Abramowitz      87
Action integral      195
Added mass      21
airy      158
Airy function      87Ч88 91 131
Airy integral      87
Akylas      128Ч139 270 382
Alfven-gravity waves      307
Alfvgn velocity      307
Amplitude equation      369 380
Anisotropic wave      103
Anticlastic surface      332
Aranha      137
Associated Legendre equation      182
Associated Legendre functions      183
Attenuation coefficient      76
Average pseudo-Lagrangian      391 393
Average variational principle      317 321 324 329
Averaged lagrangian      320Ч321 325 329 330 342 392
Axisymmetric Laplace equation      337
Axisymmetric wave equation      335
Baddour      294
Baecklund transformation      188Ч189 192 193
Bagnold      69
Barnard      137
Battjes      409
Benjamin      64 198 333 342 356 368 377 399 417Ч423 435 454Ч456 460 488
Benjamin Ч Feir instability      377Ч378 418Ч423 427 442 454
Benjamin Ч Ono equation      207
Benjamin, Bona and Mahony equation      300 306
Benney      299 351 360 370 373 399 428Ч429 433 450 457
Bergin      413 422 461
Bernoulli's equation      6 278
Bessel equation      150 153
Bessel function      30 89 105 150 153 276 282 292
Bhattacharya      254Ч255 257
Bianchi's Theorem      191
Bifurcation      464 466 467
Bifurcation, asymmetric      464 466
Bifurcation, subharmonic      464 466
Bifurcation, superharmonic      464
Bifurcation, symmetric      464 466 467
Bilinear operator      204
Bohr Ч Sommerfeld rule      187
Bona      174 306
Bottom frictional dissipation      74
Bound states      175Ч176
Boundary layer      24 71 76
Boussinesq      158
Boussinesq equation      145 155Ч156 159 173 207 306
Bowden      419
Bowen      409
Breaking condition      154
Breaking of waves      150 405Ч408 461
Bretherton      324 433
Brunt Ч Vaelsaelae frequency      306
Bryant      428
Burgers equation      371 388
Caligny      70
Campbell      26
Capillary waves      44 53 474
Capillary-gravity waves      42Ч44
Carrier      147 151Ч152
Carter      74
CASE      437
Cauchy principal value      207 235 237 292 376
Cauchy Ч Poisson problem      83Ч91
Cauchy Ч Riemann equation      189 230
Chakraborty      294
Chandrasekhar      472 483
Characteristic curves      146 151 316 401Ч402
Chen      464 466
Cherkesov      127
Chezy law of resistance      147
Chiu      437
Chu      299 350 384 442
Cleaver      412
Cnoidal wave solution      164 165 366
Cohen      428
Cokelet      408 412
Cole Ч Hopf transformation      169
Collapsing breaker      408Ч409 411
Commutation relation      194 199
Conjugate variables      197
Conservation laws      3Ч4 168Ч169 195 349 438
Conservation of energy      9 177 196 323 331
Conservation of wave action equation      323Ч324
Conserved density      168 170
Constant of motion      168Ч169
Continuity equation      3
Continuum Hypothesis      2
Couette flow      27Ч29
Courant      332 336
Crapper      65 342 439
Crapper's nonlinear capillary wave solution      65
Crawford      377Ч378 450 452 454Ч458 460
Critical curve      125
Critical velocity      82 97 105 119 123Ч128
Cylindrical wave equation      152
D'Alembert solution      145
Dagan      137Ч138
Damping gravity waves      79
Davey      299 351 355Ч358 382Ч389 394 395 442 457 487
Davey Ч Stewartson equations      354
De Broglie waves      307
de Vries      159 399
Debnath      45 57 85 92 96 97 103Ч106 115Ч128 133 163 166 196 282 294 346 348 389 394 405 444
Debye      159
Diffraction potential      280
Diffusion equation      26 70
Dipole      14 18 20 286
DiPrima      423
Dirac delta function      45 85 97 116 130 137 186 442 447
Direct scattering problem      175 181
Dispersion neutral curve      357
Dispersion relation for Alfven-gravity waves      307
Dispersion relation for capillary-gravity waves      43 56 437 480
Dispersion relation for de Broglie waves      307
Dispersion relation for dispersive waves      61 304Ч305 311 314 318 370 376 379 380
Dispersion relation for electromagnetic waves      307
Dispersion relation for gravity waves      37 40Ч42 53 55 79 88 111Ч112 139 164 213 280 306 322 328 342 350 415Ч416 419 451 471
Dispersion relation for inertial waves      307
Dispersion relation for interfacial wave      471 483
Dispersion relation for internal waves      306
Dispersion relation for magnetohydrodynamic capillary-gravity waves      102Ч103
Dispersion relation for nonlinear waves      64 325 328 342 345 347 351
Dispersion relation for Rossby waves      307
Dispersion relation for ship waves      224
Dispersion relation for water waves      306 322 328 342 347 351 369 415 416 425
Dispersive waves      38 304Ч305 311 318 370 376 379 470
Diverging wave      216 218
Djordjevic      358Ч361
Dodd      203
Donnelly      391
Doppler shift      376
Drag coefficient      273
Drag force      287
Drazin      481 485 488
Dungey      381
Dutta      163 166 346 348
Dynamic condition      7
Dynamic force      285 288
Dynamic viscosity      22 77
Dysthe      371Ч377
Dysthe's equation      373 382
Eddy resistance      219
Electromagnetic wave      307
Elliptic function      163Ч167 346 365Ч367
Elliptic integral      164
Energy density      42 58 60 61 76 225 314 317 323
Energy dissipation      32 74
Energy dissipation function      32
energy equation      9 31Ч33 323
Energy flux      9Ч10 32 61 314 317 331
Envelope soliton      442
Equation, Abel's integral      297
Equation, amplitude      369 380
Equation, associated Legendre      182
Equation, axisymmetric Laplace      337
Equation, axisymmetric wave      335
Equation, Benjamin Ч Bona Ч Mahony      300 306
Equation, Benjamin Ч Ono      207
Equation, Bernoulli      6 278
Equation, Bessel      150 153
Equation, Boussinesq      145 155Ч156 159 173 207 306
Equation, Burgers      371 388
Equation, Cauchy Ч Riemann      189 230
Equation, conservation of wave action      323Ч324
Equation, continuity      3
Equation, cylindrical wave      152
Equation, Davey Ч Stewartson      354
Equation, diffusion      26 70
Equation, Dysthe      371 374 376 382
Equation, elliptic dispersion      332 335
Equation, energy      9 31Ч33 323
Equation, energy conservation      323 331
Equation, Euler      4 101 319 389Ч391 393Ч394
Equation, Euler Ч Lagrange      196Ч198 317
Equation, evolution      136 191Ч203 359Ч361 376Ч379
Equation, forced Korteweg Ч de Vries      130 139 306
Equation, Gardner      170
Equation, Gelfand Ч Levitan Ч Marchenko (GLM)      180 182 184Ч185
Equation, Hamilton      197 313
Equation, Hamilton Ч Jacobi      313
Equation, Helmholtz      295
Equation, hyperbolic dispersion      332 335 340
Equation, inertial wave      307
Equation, interaction      432Ч438
Equation, internal wave      306
Equation, Kadomtsev Ч Petviashvilli (KP)      139 356 361
Equation, Klein Ч Gordon      306
Equation, Korteweg Ч de Vries (KdV)      130 139 157 159 161 165 168 171 174 198 201 306 370 387
Equation, Laplace      5 12 36 102 116 130 275 337 352 372 469 478 481
Equation, Lax      199 201
Equation, long water wave      306
Equation, modified Bessel      276
Equation, modified KdV      166Ч167 169 174 189
Equation, Morison      274 286 294
Equation, nonlinear Schroedinger (NLS)      136 203 207 299 345 347 351 354 385 395 418 442 444 485
Equation, operator      464
Equation, Painleve      173
Equation, Poisson      359
Equation, Rossby wave      307
Equation, Schroedinger      175 307 344
Equation, shallow water      143Ч145 148
Equation, Sine Ч Gordon      192
Equation, Sturm Ч Liouville      175 182 201
Equation, variational      326 383
Equation, vorticity transport      24
Equation, water wave      5 12 36 129 134 275 352 371 418
Equation, wave      145 201 316 400
Equation, Whitham      60Ч61 314Ч315 317 319 329 350 383Ч385
Equation, Zakharov integral      449 451 453
Ertekin      139
Estabrook      189 191 203
Euler Ч Lagrange equation      196Ч198 317
Euler Ч Lagrange operator      197Ч198
Euler's constant      293
Euler's equation      4 101 3*19 389Ч391 393Ч394
Eulerian specification      2 67
Eulerian velocity      67
Everest      212
Evolution equation      136 191Ч201 359Ч361 376Ч379
Exponential integral      233
Faltinsen      298
Feir      333 342 356 368 382 399 416 418 421 435 454 460
Ferguson      377Ч378 428
Fermi      159
Fermi Ч Pasta Ч Ulam recurrence      160 378 428
Fife      439
Figure-of-eight      399 433Ч434 443 457
Fission      186
Flaschka      208
Flux      168 315
Forced KdV equation      130 139 306
Fordy      203
Foster      26
Fourier sine transform      28
Fourier transform      28 45 78 83 111 130 240 249 446
Fox      408 412
Frechet-derivative      196Ч197
Free surface condition      7Ч8 36 42 48 62Ч63 77 83 92 116 138 237 266 275 277 352 371 430 445
Free surface elevation      6 41 45Ч46 48 50 62Ч63 77 84Ч88 213 239Ч241 249 282 298 379 429 440 447 485
Freeman      356
Frictional resistance      219
Froude      210
Froude number      50 138Ч139 218 224 239
Froude Ч Krylov force      273
Fuchs      271 281
Function, Airy      87Ч88 131
Function, associated Legendre      183
Function, Bessel      30 89 105 150 153 276 282 292
Function, Dirac delta      45 85 97 116 130 137 186 442 447
Function, elliptic      163Ч167 346 348 365Ч367
Function, energy dissipation      32 74
Function, Hamiltonian      196Ч198
Function, Hankel      276 280 292
Function, hypergeometric      336 339
Function, Jacobi elliptic      163 167 346 348
Function, Kochin H-function      231Ч232 235Ч236
Function, modified Bessel      276
Function, phase      57Ч59 150 314 319
Function, Riemann      336
Function, slowly varying      59
Function, Stokes's stream      77
Function, theta      166
Gadd      212 264
Galilean invariant      175
Galvin      148 161 406 408 410Ч411
Garabedian      338 464
Gardner      160 169 171 197
Gardner equation      170
Gardner transformation      170
Garrett      324
Garrison      271
Gauss divergence theorem      3 9 20
Gaussian curvature      113Ч114
Gelfand Ч Levitan Ч Marchenko (GLM) equation      180 182Ч185
Generalized dipole      19
Gibbon      203
Glansdorff      390Ч391
Gravity waves      36 39Ч42 53
Great wave of translation      157
Green's formula      16 291
Green's theorem      234 291
Greene      171
Greenspan      147 151Ч152
Grimshaw      370
Group velocity      4 55Ч56 101 109 306 312 334 360 372 394 414 471 482
Gruber      472
Guza      409
H-function      231Ч232 235Ч236
Hagen      30
Hagen Ч Poiseuille flow      29
Hamilton      362Ч367
Hamilton Ч Jacobi equation      313
Hamilton's variational principle      10 317
Hamiltonian      196Ч198
1 2 3
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