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Debnath L. — Nonlinear water waves
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Íàçâàíèå: Nonlinear water wavesÀâòîð: 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.
ßçûê: Ðóáðèêà: Ôèçèêà /Êîëåáàíèÿ è âîëíû /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1994Êîëè÷åñòâî ñòðàíèö: 544Äîáàâëåíà â êàòàëîã: 16.08.2005Îïåðàöèè: 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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