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Debnath L. — Nonlinear Partial Differential Equations for Scientists and Engineers
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Название: Nonlinear Partial Differential Equations for Scientists and EngineersАвтор: Debnath L. Аннотация: This book presents a comprehensive and systematic treatment of nonlinear partial differential equations and their varied applications. It contains methods and properties of solutions along with their physical significance. In an effort to make the book useful for a diverse readership, modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers is an exceptionally complete and accessible text/reference for graduates and professionals in mathematics, physics, science, and engineering. It is also suitable as a self-study/reference guide.
Язык: Рубрика: Математика /Анализ /Дифференциальные уравнения /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 593Добавлена в каталог: 06.04.2005Операции: Положить на полку |
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Riabouchinsky 340 Riccati equation 364 Richards 94 189 Riemann 219 228 287 Riemann function 75 232 Riemann initial-value problem 221 Riemann invariants 219 226 228 239—243 248 252 341 466 Robin boundary-value problem 6 Robin condition 6 Rodin 324 Roll wave 213 216—217 Roll wave equation 216 Rosales 358 Rosenau 325 Roskes 96 422 Rossby wave equation 83 266 Rowland 436 Rowlands 97 426 Ruled surface 145 Russell 331 Saddle point 304—305 Sagdeev 347 Sandri 53l Sanuki 438 Saric 97 Satsuma 98—99 Scattering data 363 370 Scattering equation 487 Scattering state 364 368 Schiff 94 Schimizu 97 Schmidt 436 Schrodinger equation 9 42—44 109 266 364 371 396 401 407 Schwarz inequality 416—417 Scoit 94—98 324 472 Secular (unbounded) term 534 Seddon 203 Segur 96 335 378 400 413 Self-focusing instability 442 Self-induced transparency (SIT) 492 Sen 90 517 Separation of variables 20—32 Separatnx 305 Serret-Frenet formulas 428 Shabat 357 395 405 413 419 422 450 Shallow water equations 236 257 339 340 Shallow water speed 35 333 339 Shallow water waves 236 257 520 Shigesada 323 Shock wave 114 166 174 192—195 230 Similarity solution 310 311 491 Similarity transformation 311 491 Similarity variable 292 311 Simple wave 179 219 222 227 229 242 Sine — Gordon (SG) equation 94 386 399 470—471 475 482 484 495—499 Single-soliton solution 375 483 Singular solution 114 153 Sinh-Gordon equation 399 498 Skyrme 95 477 487 Sleeman 98 325 Slobodkina 516 Slreiching transformation 310 Smoller 254 325 Smooth function 114 Sn-function 350 410 474 Solitary wave 335 349 410 427 Soliton 335 349 389 390 473 476 485 Solution, complete 113 Solution, discontinuous 163 178—181 Solution, general 113 Solution, generalized 3 159 174—177 Solution, particular 113 114 Solution, singular 114 153 Solution, weak 3 114 159 174—177 254 Sorensen 96 Source solution 292 Source term 302 Sparrow 328 Speed of shallow water waves 333 337 Stable node 304 Standing wave 24 Stationary phase method 58 66 268 295 Stationary point 58 66 268 295 Stewartson 96 97 98 422 Stokes 264 332 Stokes expansion 279 421 Stokes problem 84 Stokes — Ekman problem 85 Stretching variable 511 Stuart 97 98 531 Sturm — Liouville problem 393 Sturrock 531 SU 514 Superposition principle, linear 4—5 22 40 71 Superposition principle, nonlinear 389 390 486 Supersonic flow 245—247 253 Surface wave problem 87 89 Talanov 96 Taniuti 96 97 259 502 511 515 516 Tappert 97 443 Telegraph equation 8 80 83—84 232 258 thermal conductivity 52 Theta function 300 354 Three-soliton solution 380 Thyagaraja 415 Toda 95 traffic flow 189—202 Traffic flow equation 255 Traffic signal problem 198 Transform, Fourier 32 44 268 Transform, Hankel 58—59 Transform, Hilbert 97 Transform, Inverse Scattering 363—374 Transform, Laplace 49—50 Transition layer 288 293 Transition region 174 Transmission coefficient 368 Transverse vibration of string 21 Traveling wave solution 286 303 306 Triangular wave solution 294 Tricomi equation 13 260 Trullinger 482 Turin 319 Two-soliton solution 379 390 Ulam 333 418 Undular bore 350 Van Saarloos 98 Van Wijngarden 96 Variational Principle 99 104—110 Varma 97 Velocity of sound 220 Velocity potential 56 65 81 Vortex filament 428 432 Wadati 95 97 450 Wahlquist 387 389 396 Walsh 301 325 Wang 98 Ward 99 Washimi 96 97 502 Water wave equations 107 Watson 531 Wave diffraction 444 Wave energy 418 Wave equation 3 7 16 21 34 47 55 60 62 73—77 79 94 104 110 238 242 394 439 493 Wave front 153 Wave propagation velocity 187 Wave, Alfven gravity 266 Wave, cnoidal 350—351 Wave, compression 164 208 Wave, de Broglie 266 Wave, diffusive 285 288 Wave, dispersive 264 Wave, electromagnetic 9 Wave, expansive 163 170 179 207 Wave, flood 202 203 Wave, generalized simple 250—252 Wave, gravity 65 265 410 Wave, incident 368 Wave, inertial 266 Wave, internal 265 Wave, internal-inertial 266 Wave, ion-acoustic 344 346 518 Wave, kinematic 185—187 Wave, N 296 297 Wave, nondispersive 265 Wave, reflected 368 Wave, refractive 163 179 Wave, roll 213 216—217 Wave, Rossby 83 266 Wave, shallow water 236 520 Wave, shock 114 166 174 192 230 Wave, simple 179 219 222 227 229 Wave, solitary 335 349 410 427 Wave, standing 24 Wave, Stokes 263 280 Wave, transmitted 368 Wave, water 265 280 Weak solution 3 114 159 172 174—177 254 Wei 502 511 513—514 Weidman 96 335 Weiland 97 Well posed problem 6 17 Wenlzcl 441 West 320 Whilham 94 105 107—108 185—189 267 275 281 293 296 353 355 409 418 459 468 Whitham averaged Lagrangian 277 468 Whitham averaged variational principle 276—277 282 469 Whitham equation 271—273 276 278 282 404 421 Whitham rule 193 296 Wilhelmson 97 wronskian 369 Yajima 96 413—415 502 516 Yang — Mills equations 99 Yuen 96 418 Zabusky 96 334—335 352 359 418 Zakharov 96 347 395 405 413 419 422 450 Zakharov equation 435 Zakharov — Shabat (ZS) scheme 395 Zel'dovich 324 326 Zeppetella 325
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