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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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Abdelkader 325 Ablowitz 96 99 325 400 413 Absorption isotherm 205 Acoustic radiation problem 62—64 Acrivos 97 Adiabatic invariant 463 airy 332 Airy differential equation 442 Airy function 36 358 Airy integral 36 AKNS method 400—401 Alfven wave velocity 266 Ammerman 95 302 Antikink 336 474 477 Antisoliton 473 474 477 483 Aoki 95 301 Arecchi 95 Aris 95 Arnold 95 301 Aronson 323 Asano 97 502 511—512 515 526 Associated Legendre equation 376 Associated Legendre function 376 Asymptotically stable 306 Average conservation equation 464 Average Lagrangian 468 470 Average variational principle 469 Axisymmetric acoustic radiation problem 62 Axisymmetric diffusion equation 61 Axisymmetric wave equation 60 Backlund transformation 386—388 403 450 484 Balmforth 98 Barenblatt 324—326 Barone 95 Ben Jacoh 98 Benjamin 97 98 280 418 Benjamin — Bona — Mahony (BBM) equation 97 265 401 Benjamin — Feir (modulational) instability 424 426 Benjamin — Ono (BO) equation 97 Benney 96 422 Benton 324 Berezin 351 352 Bernoulli — Euler equation 90 Bespalov 96 Bessel function 59 62 Bhatnagar 516 Bianchi theorem 389 Biharmonic equation 9 64 86 Birkhoff 309 Birkhoff theorem 418 Bjackstock 324 Blasius problem 85 328 Bleakney 23 [ Bohr — Sommerfeld rule 385 Boltzmann constant 344 Boltzmann distribution 345 518 Boltzmann nonlinear diffusion problem 312 326 Boltzmann transformation 314 Bore 238 Born — Infeld equation 107 Bound state 364—366 483 Boundary-value problem 5 59 Boussinesq 332 Boussinesq equation 9 95 108 265 333 339 341 357 533 Brauner 324 Breakers 203 Breather solution 481 482 Bright soliton 414 Brillouin 441 Britton 325 Brunt — Vaisala frequency 266 Burgers 95 284 296 Burgers equation 95 200 256 284 285 289 518 Burgers — Huxley equation 98 Burton 231 Cannonical form 10 Cannonical transformation 148 Canosa 325 CASE 324 Cauchy condition 5 Cauchy data 120 124—125 131 242 Cauchy principal value 97 Cauchy problem 5 16—17 34 39 47 50 80 88 119—120 130 131 141 157 158 178 Cauchy — Poisson problem 56 64 81 89 Cauchy — Riemann equations 387 Caustic 441 Cavali — Sforva 95 302 Characteristic base curve 117 Characteristic curves 11 117 118 224—225 340 Characteristic direction 116 136 Characteristic equation 11 117 137 Characteristic shock 253 Characteristic strip 139 Characteristic strip equations 139 Characteristic velocity 279 281 467 Characteristics 11 117 238 Charpit equations 137 139 142 Chen 96 99 Chezy formula 202 Chiu 324 Chromatographic models 204—208 Chu 96 282 421 Clairaut equation 140 141 144 Classical solution 3 Cnoidal wave 350—351 Cole 289 301 Cole — Hopf transformation 289 361 Column isodierm 205 Commutator 392 Complete elliptic integral 350 Complete integral 113 Complete solution 113 Compression wave 164 208 Conjugate variables 148 Conservation equations 172—173 319 463 Conservation laws 159 160—161 186 359 419 517 Conservation of energy 369 Conserved densities 360 Continuity equation 186 209 214 219 344 Continuous spectrum 368 Convolution 33 Convolution theorem 33—34 Cornish 216 Courant 247 Cramer 517 Crandell 383 403 Crank 316 323 Crighton 324 Cylindrical KdV equation 402 D'Alembert solution 17 35 76 244 339 Darcy law 254 Dark soliton 414 448 Davey 96 422 Davis 97 491 de Broglie wave 266 De Leonardis 482 de Vries 96 333 Debnath 52 56—57 59 64—66 81—82 86 89 96 100 233 278 280 337 350 354 409 411 413 454 474 Debye 333 Debye length 345 density 186 359 Derivative expansion method 531 Developable surface 145 Dielectric constants 439 Diffusion coefficient 25 212 310 Diffusion equation 7 25 27 39 46 51—54 61 68—69 84—85 90 284 289—290 310 312 316 319—320 diffusion length 256 Diffusion-reaction equation 302 319—320 Diffusive wave 285 288 Dipole solution 298 Dirac delta function 32—33 37 40 62 Dirichlet condition 5 Dirichlet problem 5 29 36 45 102 Discontinuous solution 165 172 178—181 dispersion relation 264 278 407 441 443—444 446 497 516 Dispersion relation dispersive wave 264 Dispersion relation for Alfven gravity wave 266 Dispersion relation for cnoidal wave 351 Dispersion relation for de Broglie wave 43 266 Dispersion relation for electromagnetic wave 266 Dispersion relation for ion-acoustic wave 346 Dispersion relation for nonlinear wave 278 Dispersion relation for solitary wave 410 Dispersion relation for string wave 516 Dispersion relation for water waves 65 265 410 Dodd 396 Drazin 379—380 384 478 Dressier 216—217 218 Dunbar 325 Dutta 350 354 409 411 474 Effective mode 418 Eigenfunctions 22 26 28 Eigenvalues 22 26 28 Eikonal equation 151 155 441 Ekman layer 85 Elastic particles 482 Elastic wave equation 110 Electrical susceptibility 439 Electromagnetic wave equation 9 Electron plasma frequency 345 Elliptic equation 12 13 Elliptic integral 350 409 Energy density 272 275 Energy flux 272 275 Engelbrecht 515 Entropy criterion 180 Envelope 129 Envelope soliton 336 413—414 526 Enz 95 Equation, associated Legendre 376 Equation, axisymmetric wave 60 Equation, Benjamin — Bona — Mahony (BBM) 97 265 401 Equation, Benjamin — Ono (BO) 97 Equation, Bernoulli — Euler 90 Equation, biharmonic 9 64 86 Equation, Bom — Infeld 107 Equation, Boussinesq 9 95 108 265 333 339 341 357 533 Equation, Burgers 95 200 256 284 285 289 502 518 Equation, Burgers — Huxley 98 Equation, Cauchy — Riemann 387 Equation, characteristic 11 117 137 Equation, Charpit 137 139 142 Equation, Clairaut 140 141 144 Equation, conservation 172 173 319 463 Equation, continuity 186 214 219 344 Equation, cylindrical KdV 402 Equation, diffusion 7 25 27 39 46 51—54 61 68—69 84—85 90 284 289 290 310 312 316 319—320 Equation, diffusion-reaction 302 319—320 Equation, dynamical 462 Equation, eikonal 151 155 441 Equation, elastic wave 110 Equation, electromagnetic wave 9 Equation, elliptic 12 13 Equation, Euler 120 257 277 282 Equation, Euler — Darboux 19 Equation, Euler — Lagrange 100—102 104 109 276 Equation, Euler — Poisson — Darboux 234 260 Equation, evolution 392 395 505 508 Equation, Fisher 95 301 Equation, Gardner 362 Equation, Gelfand — Levitan — Marchenko (GLM) 373 374 375 377 Equation, Ginzburg — Landau (GL) 98 Equation, glacier flow 211 Equation, Hamilton 103 146 Equation, Hamilton — Jacobi 145—147 274 Equation, heat 7 51 Equation, Helmholtz 8 63 71 73 80 Equation, hyperbolic 11-13 231 284 Equation, hypergeometric 232 Equation, internal wave 265 Equation, internal-inertial wave 266 Equation, Kadomtsev — Petviashvilli (KP) 99 402—403 Equation, KdV — Burgers 502 Equation, kinematic wave 94 161 186 202 465 Equation, Klein — Gordon (KG) 8 80 91 94 104 265 426 453 456 458 460 496—497 Equation, Korteweg — de Vries (KdV) 9 35 333—334 343 347 356 358 360 363 398 403 449 517 519 521 539 Equation, Lagrange 102—103 Equation, Laplace 8 36 38 45 56 59 61 65 79 90 101 387 Equation, Lax 392—393 400 403 Equation, linear partial differential 2—3 111 Equation, linear scattering 487 Equation, linear wave equation 7 21 34 242 Equation, Maxwell 344 438—439 Equation, minimal surface 102 Equation, modified KdV (mKdV) 96 354—355 361 399 403 515 517 Equation, Navier — Stokes 214 Equation, nonlinear diffusion 284 312 314 316 Equation, nonlinear diffusion-reaction 319 Equation, nonlinear partial differential 3 93 111 112 270 Equation, nonlinear Schrodinger (NLS) 96 282 396 398 402 408 410 412 415 422 424 431 436 438 447 448 451 482 525 526 533 Equation, nonlinear wave equation 94 238 Equation, Painleve 357 491 Equation, parabolic 12 284 Equation, paraxial 444 Equation, Peregrine 520 Equation, Poisson 8 70 109 Equation, Prandtl — Blasius 328 Equation, quasi-linear partial 2 111 282 Equation, Riccati 364 Equation, roll wave 216 Equation, Rossby wave 83 266 Equation, Schrodinger 9 42—44 109 266 364 371 396 401 407 Equation, shallow water 236 257 339 340 Equation, sine-Gordon (SG) 94 386 399 470—471 482 484 495 499 Equation, sinh-Gordon 399 498 Equation, telegraph 8 80 83—84 232 258 Equation, traffic flow 255 Equation, Tricomi 13 260 Equation, water wave 107 Equation, wave 3 7 16 21 34 47 55 60 62 73—77 79 94 104 110 238 242 439 493 Equation, Whitham 271—273 276 278 282 404 421 Equation, Yang — Mills 99 Estabrook 387 389 396 Euler equation 120 257 277 282 Euler — Darboux equation 19 Euler — Lagrange equation 100—102 104 109 276 Euler — Poisson — Darboux equation 234 260 Evolution equation 392 395 502 505 508 Expansive wave 163 170 179 207 Fan 194 207 Fan centered 194—195 Feir 280 418 Ferguson 418 Fermi 333 418 Fermi — Pasta — Ulam (FPU) recurrence 334 418 Fife 95 323 325 Fisher 95 301 Fisher equation 95 301 Fission 381 FitzHugh 98 Flood wave 202 203 Flux 159 186 359 Flux transport 319 Focusing instability 448 Forcing term 264 Fordy 396 Fourier method 5 21 Fourier solution 47 Fourier transform 32 44 268 Fractional derivative 52—53
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