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Debnath L. — Nonlinear water waves
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Íàçâàíèå: Nonlinear water waves
Àâòîð: Debnath L.
Àííîòàöèÿ: 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.
ßçûê:
Ðóáðèêà: Ôèçèêà /Êîëåáàíèÿ è âîëíû /
Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö
ed2k: ed2k stats
Ãîä èçäàíèÿ: 1994
Êîëè÷åñòâî ñòðàíèö: 544
Äîáàâëåíà â êàòàëîã: 16.08.2005
Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Abel integral equation 297
Ablowitz 193 361 362 363
Abramowitz 87
Action integral 195
Added mass 21
airy 158
Airy function 87—88 91 131
Airy integral 87
Akylas 128—139 270 382
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 320—321 325 329 330 342 392
Axisymmetric Laplace equation 337
Axisymmetric wave equation 335
Baddour 294
Baecklund transformation 188—189 192 193
Bagnold 69
Barnard 137
Battjes 409
Benjamin 64 198 333 342 356 368 377 399 417—423 435 454—456 460 488
Benjamin — Feir instability 377—378 418—423 427 442 454
Benjamin — Ono equation 207
Benjamin, Bona and Mahony equation 300 306
Benney 299 351 360 370 373 399 428—429 433 450 457
Bergin 413 422 461
Bernoulli's equation 6 278
Bessel equation 150 153
Bessel function 30 89 105 150 153 276 282 292
Bhattacharya 254—255 257
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 — Sommerfeld rule 187
Bona 174 306
Bottom frictional dissipation 74
Bound states 175—176
Boundary layer 24 71 76
Boussinesq 158
Boussinesq equation 145 155—156 159 173 207 306
Bowden 419
Bowen 409
Breaking condition 154
Breaking of waves 150 405—408 461
Bretherton 324 433
Brunt — Vaelsaelae frequency 306
Bryant 428
Burgers equation 371 388
Caligny 70
Campbell 26
Capillary waves 44 53 474
Capillary-gravity waves 42—44
Carrier 147 151—152
Carter 74
CASE 437
Cauchy principal value 207 235 237 292 376
Cauchy — Poisson problem 83—91
Cauchy — Riemann equation 189 230
Chakraborty 294
Chandrasekhar 472 483
Characteristic curves 146 151 316 401—402
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 — Hopf transformation 169
Collapsing breaker 408—409 411
Commutation relation 194 199
Conjugate variables 197
Conservation laws 3—4 168—169 195 349 438
Conservation of energy 9 177 196 323 331
Conservation of wave action equation 323—324
Conserved density 168 170
Constant of motion 168—169
Continuity equation 3
Continuum Hypothesis 2
Couette flow 27—29
Courant 332 336
Crapper 65 342 439
Crapper's nonlinear capillary wave solution 65
Crawford 377—378 450 452 454—458 460
Critical curve 125
Critical velocity 82 97 105 119 123—128
Cylindrical wave equation 152
D'Alembert solution 145
Dagan 137—138
Damping gravity waves 79
Davey 299 351 355—358 382—389 394 395 442 457 487
Davey — Stewartson equations 354
De Broglie waves 307
de Vries 159 399
Debnath 45 57 85 92 96 97 103—106 115—128 133 163 166 196 282 294 346 348 389 394 405 444
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 61 304—305 311 314 318 370 376 379 380
Dispersion relation for electromagnetic waves 307
Dispersion relation for gravity waves 37 40—42 53 55 79 88 111—112 139 164 213 280 306 322 328 342 350 415—416 419 451 471
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 102—103
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 38 304—305 311 318 370 376 379 470
Diverging wave 216 218
Djordjevic 358—361
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 371—377
Dysthe's equation 373 382
Eddy resistance 219
Electromagnetic wave 307
Elliptic function 163—167 346 365—367
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 31—33 323
Energy flux 9—10 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 — Bona — Mahony 300 306
Equation, Benjamin — Ono 207
Equation, Bernoulli 6 278
Equation, Bessel 150 153
Equation, Boussinesq 145 155—156 159 173 207 306
Equation, Burgers 371 388
Equation, Cauchy — Riemann 189 230
Equation, conservation of wave action 323—324
Equation, continuity 3
Equation, cylindrical wave 152
Equation, Davey — Stewartson 354
Equation, diffusion 26 70
Equation, Dysthe 371 374 376 382
Equation, elliptic dispersion 332 335
Equation, energy 9 31—33 323
Equation, energy conservation 323 331
Equation, Euler 4 101 319 389—391 393—394
Equation, Euler — Lagrange 196—198 317
Equation, evolution 136 191—203 359—361 376—379
Equation, forced Korteweg — de Vries 130 139 306
Equation, Gardner 170
Equation, Gelfand — Levitan — Marchenko (GLM) 180 182 184—185
Equation, Hamilton 197 313
Equation, Hamilton — Jacobi 313
Equation, Helmholtz 295
Equation, hyperbolic dispersion 332 335 340
Equation, inertial wave 307
Equation, interaction 432—438
Equation, internal wave 306
Equation, Kadomtsev — Petviashvilli (KP) 139 356 361
Equation, Klein — Gordon 306
Equation, Korteweg — 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 166—167 169 174 189
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 143—145 148
Equation, Sine — Gordon 192
Equation, Sturm — 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 60—61 314—315 317 319 329 350 383—385
Equation, Zakharov integral 449 451 453
Ertekin 139
Estabrook 189 191 203
Euler — Lagrange equation 196—198 317
Euler — Lagrange operator 197—198
Euler's constant 293
Euler's equation 4 101 3*19 389—391 393—394
Eulerian specification 2 67
Eulerian velocity 67
Everest 212
Evolution equation 136 191—201 359—361 376—379
Exponential integral 233
Faltinsen 298
Feir 333 342 356 368 382 399 416 418 421 435 454 460
Ferguson 377—378 428
Fermi 159
Fermi — Pasta — Ulam recurrence 160 378 428
Fife 439
Figure-of-eight 399 433—434 443 457
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 196—197
Free surface condition 7—8 36 42 48 62—63 77 83 92 116 138 237 266 275 277 352 371 430 445
Free surface elevation 6 41 45—46 48 50 62—63 77 84—88 213 239—241 249 282 298 379 429 440 447 485
Freeman 356
Frictional resistance 219
Froude 210
Froude number 50 138—139 218 224 239
Froude — Krylov force 273
Fuchs 271 281
Function, Airy 87—88 131
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 163—167 346 348 365—367
Function, energy dissipation 32 74
Function, Hamiltonian 196—198
Function, Hankel 276 280 292
Function, hypergeometric 336 339
Function, Jacobi elliptic 163 167 346 348
Function, Kochin H-function 231—232 235—236
Function, modified Bessel 276
Function, phase 57—59 150 314 319
Function, Riemann 336
Function, slowly varying 59
Function, Stokes's stream 77
Function, theta 166
Gadd 212 264
Galilean invariant 175
Galvin 148 161 406 408 410—411
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 113—114
Gelfand — Levitan — Marchenko (GLM) equation 180 182—185
Generalized dipole 19
Gibbon 203
Glansdorff 390—391
Gravity waves 36 39—42 53
Great wave of translation 157
Green's formula 16 291
Green's theorem 234 291
Greene 171
Greenspan 147 151—152
Grimshaw 370
Group velocity 4 55—56 101 109 306 312 334 360 372 394 414 471 482
Gruber 472
Guza 409
H-function 231—232 235—236
Hagen 30
Hagen — Poiseuille flow 29
Hamilton 362—367
Hamilton — Jacobi equation 313
Hamilton's variational principle 10 317
Hamiltonian 196—198
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