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Debnath L. — Nonlinear Partial Differential Equations for Scientists and Engineers
Debnath L. — Nonlinear Partial Differential Equations for Scientists and Engineers



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Название: Nonlinear Partial Differential Equations for Scientists and Engineers

Автор: 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: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 593

Добавлена в каталог: 06.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Freeman      99 402
Frenkel      95
Friedricbs      247
Froude number      216 218
Fulton      97
Functional      99—101
Fundamental harmonic      23
Fundamental parameters      337 344
Fundamental period      23
Fundamental solution      39—40 292 314
Galvin      335
Gardner      335 361 363 506 514
Gardner equation      362
Gardner transformation      361
Gardner — Morikawa transformation      506 511 513
Gazdag      325
Gelfand — Levitan — Merchenko (GLM) equation      373 374 375 377
General integral      113
General solution      3 113
Generalized NLS equation      438 526
Generalized Rankine — Hugoniot shock condition      253
Generalized Riemann invariants      252
Generalized simple wave      250—252
Generalized solution      3 159 174
Geometrical optics approximation      460
Ghez      323
Gibbon      95 396
Gibbons      415 436
Ginzburg — Landau (GL) equation      98
Glacier flow      2l0—211
Goldstein      150
Gordon      8
Gorschkov      531
Gorter — Mellink law      318
Gravity wave      65 265 410
Green signal problem      196
Green's function      39—40 67—78 91 453—459
Griffith      231
Grindrod      325
Group velocity      97 265 273 280
Growth rate      301
Growth term      161
Gurney      323
Gurtin      323
Haberman      96
Hadamard example      6
Hagstrorn      325
Hahn      492—494
Haight      189
Hamilton density      482—483
Hamilton equations      103 146
Hamilton function      102
Hamilton principal function      145
Hamilton variational principle      102 104 276 531
Hamilton — Jacobi equation      145—147 150 151 274
Hamiltonian      102 145 150
Hammack      335 413
Hankel transform      58—59
Hasegawa      97 443
Hasimoto      96 422 428 431 531
Hassan      531
Heat equation      7 51
Helmholtz equation      8 63 71 73
Hilbert space      366 392—394
Hilbert transform      97
Hirota      335
Hodgkin and Huxley equation      98
Hodograph transformation      247
Hopf      289
Hoppenstradt      307
Howard      320
Hydraulic jump      203 238
Hyperbolic equation      11—13 231—233 284
Hypergeometric equation      232
Hypergeometric function      232
Ichikawa      97
Illposed problem      6 280
Index of refraction      151
Infeld      96 344 436
Initial-value problem      5—6 17 81 82 119 161 163—174 178 221 267 285 289 363 392
Inoue      537
instantons      99
Integrability condition      137
Integral surface      4 116
Interaction strength      418
Internal wave equation      265
Internal-inertial wave equation      266
Inverse Fourier transform      32 44
Inverse Hankel transform      59
Inverse Laplace transform      49
Inverse scattering transform      363—374 487
Ion-acoustic wave      344 346 518
Ion-plasma frequency      345
Isentropic flow      222 257 260
Isothermal curves      37
Jacobi cn-function      350 351
Jacobi dn-function      411
Jacobi elliptic function      350 410 474
Jacobi sn-function      350 410 474
Jacobi theia function      300 354
Johnson      96 99 325 379—380
Jones      268 325
Josephson      95
Jost solutions      371
Jump condition      173 174
Jump discontinuity      177 314
Kadomtsev      99
Kadomtsev — Petviashvili (KP) equation      99 402—403
Kako      96
Kakutani      96 502 515
Kaliappan      321
Kametaka      325
Karpman      97 35J 385 436
Kaup      396 400 482
Kawahara, SIS      531 533
KdV — Burgers equation      502
Keller      325
Kelley      96
Kerr effect      442
Kinematic wave      185—187
Kinematic wave equation      94 161 186 202 465
kinetic energy      25 43 110
Kink      336 473 476 485
Kirchhoff transformation      316
Klein      8
Klein — Gordon (KG) equation      8 80 91 94 104 105 265 426 453 456 458 460 496—497
Kleitz — Seddon law      204
Kolmogorov      95 302
Konno      450
Kontorova      95
Kopell      320
Korteweg      96 333
Korteweg — de Vries (KdV) equation      9 35 265 333—334 343 347 356 358 360 363 398 403 449 517 519 521 539
Kramers      441
Kriess      324
Kroneker delta      23
Krushkal      97
Kruskal      334—335 361 418
Kulikovskii      5J6
Kynch      94 208 256
Lagrange bracket      149—150
Lagrange equation      102—103
Lagrangian      102—105 107
Lagrangian density      104 467 482
Lagrangian stability      417
Lake      96 418
Lamb      95 482 487 489 491 498
Lame constants      80
Landau      383
Langmuir soliton      433
Langmuir, isotherm model      206
Laplace equation      8 36 38 45 56 59 61 65 79 90 101 387
Laplace transform      49—50
Laplacian      42 338
Lardner      324
Larson      307 324
Lax      181 250—253 335 391
Lax entropy criterion      180 253
Lax equation      392—393 400 403
Lax pair      392 403
Le Veque      254
Leffrey      252 259 441 515 533
Legendre polynomial      376
Leibovich      96 53S
Lie group      310 356—357
Lifshitz      383
Lighthill      94—95 108 185—189 211 278 280 324
Linear operator      2 67
Linear partial differential equation      2 3 11l
Linear scattering equation      487
Linear wave equation      7 21 34 242
Liu      96 99
Local frequency      269—270 273
Local Mach number      246
Local wavenumber      269—270 273
Logan      325
Lorenz      324
Luke      105 107
MA      450
MacCarny      323
Mach line      246
Mach number      156 246
Madsen      96
Magnetic permeability      439
Magnetic wave equation      439
Makhankov      336
Manning formula      203
Manoranjan      325
Matrix operators      395
Matsumoto      537
Max worthy      335
Maxwell equations      344 438—439
McCall      492—494
McKean      325
Mean value properly      31
Mei      96 282 421
Mersenne law      23
Method of characteristics      118 135
Method of multiple scale      531—540
Minimal surface equation      102
Mitchell      325
Miura      361 364 401
Miura transformation      361 364
Modified KdV (nKdV) equation      96 354—355 361 399 403 515 517
Modulational instability      424 426
Mollenauer      443
Moment of instability      342
Monge axis      116
Mongecone      117 136—137
Monochromatic wave      440
Monoclinal flood wave      203
Montroll      320
Morikawa      506
Multiple Fourier transform      44
Munier      316
Murray      314 322—325
N-soliton solution      376
N-wave solution      296 297
Naguma      98
Navier — Stokes equations      214
Nayfeh      97 531
Neumann boundary-value problem      6 38 88
Neumann condition      6
Newell      400 482
Newman      320—324
Nisbet      323
Nishihara      516
nodes      24
Nondispersive wave      265
Nonlinear diffusion equation      284 312 314 316
Nonlinear diffusion-reaction equation      319
Nonlinear Dirichlet problem      102
Nonlinear evolution equation      392 395
Nonlinear group velocity      280
Nonlinear Klein — Gordon (KG) equation      94 104 426 496
Nonlinear partial differential equation      3 93 111 112 270
Nonlinear Schrodinger (NLS) equation      96 282 396 398 402 408—410 412 415 422 424 431 436 438 447 448 451 482 525—526 536
Nonlinear superposition principle      389—390 486
Nonlinear wave equation      94 238
Normal dispersion      448
Normal modes      23
Nozaki      516
Nwogo      96
Nye      94 210
Oikawa      415 516
Okubo      314
Ono      97 422 502 511 515 531
Order      2
Ostrovsky      502 527 530
Outi      413
overtones      23
PACK      231
Painleve equation      357 491
Parabolic equation      12 284
Paraxial equation      444
Parker      324
Partial differential equation      2
Particular solution      113 114
Pasta      333 418
Pattle      320
Pawlik      97
Pelinovsky      502 527 530
Penel      324
Peregrine      95—96 449 450 520
Peregrine equation      520
Perring      477 487
Petviashvili      99
phase velocity      97 264 404
Phillips      451
Piston problem      227 234
Planck constant      8 42 266 386
Plateau problem      101
Platzman      324
Poincare theorem      148
Point of inflexion      321
Poisson bracket      147
Poisson equation      8 70 109
Poisson integral formula      31 36 40
Poisson kernel      32
Polarization      439
Poly tropic gas      228
Potential      365 400 422 487
potential energy      25 43 110
Prandtl — Blasius problem      327 428
Prasad      96—97 516 538
Prolongation structure method      396
Quasi-linear partial differential equation      2 108 111 282
Raizer      324
Rankine-Hugoniot condition      174 253
Ravindran      96—97 538
Rayleigh      332
Rayleigh problem      85
Rayleigh quotient      416
Reaction term      161 302
Redekopp      96
Reductive perturbation method      502
Reflection coefficient      368
Refractive index      440
Refractive wave      163 179
Reynolds number      291 297 299
1 2 3
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