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Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed) — Introduction to Symmetry Analysis
Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed) — Introduction to Symmetry Analysis



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Название: Introduction to Symmetry Analysis

Авторы: Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed)

Аннотация:

This text offers a broad, self-contained, introduction to the basic concepts of symmetry analysis and is intended primarily for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. The software requires Mathematica 2.2 or higher. MathReader 4.0 is included to permit the user without access to Mathematica to read the sample notebooks and follow the procedure used to find symmetries.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 654

Добавлена в каталог: 27.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Lifshitz, E.M.      97 120 310 317 329 362 514
Lighthill, M.J.      95
Linear flows in three dimensions      88
Linear flows in two dimensions      85
Liouville equation      517
Liouville equation cross derivative form      517
Lorentz group      146 206
Lorentz transformation      6 12
Lumley, J.I.      444
Ma, P.K.H      303 317
Mach number      46 47 385
Magee, C.J.      550
Magnetostatics analogy      333
Mahalingham, S.      273 275
Make Commutator Table      599
Make Rules Array      598
Mansour, N.      444 445
Mars atmosphere      42
Matrix invariants      84 85 88 340 345 429
Matrix inverse      242 434
McLachtan, B.G.      53 54
McMahon, T.A.      51 54
Meleshko, S.V      375 394
Method of canonical coordinates      215
Method of differential invariants      216 222 226 230 310
Method of Lagrange      70 82 204
Method of Lagrange and Charpit      74
Method of variation of parameters      228
Miller, D.G.      46 48 54
Miura transformation      541
Miura, R.M.      541 551
Mixing layer      397
Moftat, H.K.      329 362
Momenta generalized      101
Monatomic gas      374 392
Moser, R.D.      427 430 444 445
Multi-parameter group      134 157 217
Multipole expansion      333
Navier — Stokes equations      30 318 393
Navier — Stokes equations invariant groups      319
Navier — Stokes equations microscales      419
Newton’s law      96
Nieuwstadt, F.T.M.      550
Nodal point      348
Noether symmety      504
Noether, A.E.      498 513
Noether’s theorem      119 504 513
Non-abelian      9
Non-classical symmetries      269
Non-local group      515 521 528
Non-local group Burgers equation      527
Non-local group KdV potential equation      535 538
Non-uniform translation group      319 320
Nonlinear critical points      87
Nonlinear diffusion      293
Nonlinear eigenvalue problem      266
Nonlinear superposition law for the KdV equation      546
Nonlinear superposition law for the sine-Gordon equation      521 546
Nonlinear wave equation      275 534
Notation      15 23 24 101 178 181 183 240 250
Notation for “dimensions of”      35
Null algebra      136
Null element      144
Nussbaum, A.      30 32
Oberlack, M.      443 445
Olver, P.      3 31 447 479 497
Once-extended finite group      193 239
Once-extended infinitesimal group      197 242
One parameter shear flows      401
One parameter shear flows table of      408
One-parameter Lie group      13 123
One-parameter Lie group definition of      123
Orbit      113 115
Orbital period      115
Ordinary differential equations      191 203
Ordinary differential equations first order      57 62 121 191 203
Ordinary differential equations higher order      221
Ordinary differential equations second order linear      209
Ordinary differential equations second order, nonlinear      225 234 235
Orthogonal functions      262
Oswatitsch, K.      95
Overdamped      117
Ovsiannikov, L.V.      3 31 364 369 393
Parabolic cylinder functions      262 268
Partial differential equations      237
Partial differential equations fourth order      513
Partial differential equations linear, first order      55 57 61 70 121
Partial differential equations nonlinear, first order      74 82
Partial differential equations second order      496
Particle path equations      339 351 404 441
Particle path equations in similarity coordinates      404
Particle path equations in three dimensions      69
Particle path equations in two dimensions      68
Particle path equations Landau — Squire jet      337 338 344
Particle path equations low Reynolds number jet      346
Particle path equations turbulent vortex ring      418
Particle path equations unsteady dipole      345
Pathline of a group      122
Pendulum, simple      93
Pendulum, spherical      119
Perfect differential      57 60 63 80
Perigee      114
Perihelion      115
Permeability      263
Permutahility theorem      521
Perry, A.E.      95 445
Perturbation velocity potential      386
Petviashvili, V.I.      551
Pfaffian 1-form      58 72 155 168
Pfaff’s theorem      59 66 73 157
Phase plane analysis      85 284 287
Phase portrait      83 287 318
Phase portrait bifurcation      330 349
Phase portrait impulsively started jet      348 349 350
Phase portrait turbulent vortex ring      418
Phase space      83 293 318
Plane laminar jet      361 438
Plane mixing layer      396 406
Plane turbulent jet      402 438
Planets, table of      36
Point explosion      375
Point symmetry, point group, point transformation      56 178 185 237
Poisson brackets      103 104
Poisson equation      74 331
Poisson equation for pressure      353
Pollack, J.      54
Porosity      263
Porous medium      264
potential energy      110
Potential equation      521
Potential function      60 385 523
Power monomial function      48
Prandtl — Glauert rule      389
Pressure      42 44 63
Pressure coefficient      384 385 390
Pressure distribution      384 386
Pressure far field      334
Principle of least action      98 99
Production of turbulent kinetic energy      400
Projective group      135 137 145 208
Prolongation      200
Prolonged group      200 245 558 562
Prolonged group operator      200 245 558 563
Prolonged versus extended group      200
Proper Lie — Backlund symmetry      462 486 494
Pthinfinitesimal      597
Pukhnachov, V.V.      31 323 362 393
Quadratic discriminant      85 117
Quadrature, integration by      57 62 63 156 162 230
Quarter chord point      304
Racing shell      51
Radial vorticity function      344
Raizer, Y.P.      375 394
Rale-of-roialion      426
Rate-ot-strain      426
Ratio of specific heats      382
Rational root, elliptic curve      173 177 349 353 356
Recursion operators      478
Recursion operators Burgers equation      486
Recursion operators Burgers potential equation      481 497
Recursion operators heat equation      479
Recursion operators integro-differential      486
Recursion operators KdV equation      490
Reduced mass      110
Reflection      8
Reflectional symmetry      9
Reid, G.J.      599
Remoissenet, M.      534 547 550
Rennich, S.C.      31
Restricted Euler equation      432 442
Reversible process      67
Reynolds averaged Navier — Stokes equations      398 399
Reynolds decomposition      397
Reynolds number boundary layer      279 284 329
Reynolds number Burgers equation      523
Reynolds number circular Couette flow      330
Reynolds number Falkner — Skan sink flow      308
Reynolds number flow past a circular cylinder      42 43 53
Reynolds number flow past a sphere, compressible      45 48
Reynolds number flow past a sphere, incompressible      41
Reynolds number incompressible flow      318
Reynolds number invariance      395 397 400 401
Reynolds number invariance group interpretation      401
Reynolds number Jeffrey — Hamel flow      326
Reynolds number round jet      335 336 339 343 346 348
Reynolds number scaling      407
Reynolds number Taylor microseale      414 420
Reynolds number turbulent vortex ring      413 419
Reynolds stresses      398
Reynolds, O.      397 444
Reynolds, W.C.      427 445
Ribet, K.A.      173 177
Ricatti equation      120 204 213 232
Ricatti equation solution      205
Rodionov, A.A.      31 393
Rogers, C.      3 31 516 550
Rogers, M.M.      427 430 444 445
Roshko, A.R.      xix 394 396 444
Rotation group      7
Rotation group in 2D once extended      225
Rotation group in three dimensions, SO(3)      148 505
Rotation group in two dimensions, SO(2)      7 131 133 149 153
Rotation invariants      434
Rott, N.      445
Runge — Kutta      132 147
Runge — Lenz vector      510
Saddle      86 288 296 348 417
Saffman, P.      332 363 394
Sagan, C.      54
Sands, M.      32
Schoppa, W.      445
Schwarz, F.      32
Scott, A.C.      550
Second order ODE invariant under a given group      213
Second order ODEs, table of      214
Second Term      597
Sedov, L.I.      375 394
Segev, M.      534 550
Semenova, I.B.      362
Series solution of the determining equations      209 251
Shallow water approximation      371
Shock wave      45 375
Shu, D.      53 54
Similarity rules      395 403
Similarity rules, inertial subrange      411
Similarity rules, vortex ring      416
Similarity variables      19
Similarity variables Blasius boundary layer      282
Similarity variables diverging channel flow      326
Similarity variables Falkner — Skan boundary layers      307 357
Similarity variables Falkner — Skan sink flow      308
Similarity variables heat equation      19 20 260
Similarity variables homentropic equations      372
Similarity variables nonlinear diffusion equation      294
Similarity variables spherical blast wave      380
Similarity variables turbulent vortex ring      417
Similarity variables unsteady round jet      338
Sine-Gordon equation      519 521
Single hump solution, KdV equation      543
Singular solution      77 79
Skan, S.W.      317
Skin friction coefficient      52 288
Snook, K.      54
Sobel, D.      xli
Solitary wave Korteweg de Vries equation      533
Solitary wave sine-Gordon equation      521
Soliton      521
Solvable Lie algebra      139 140 141 142 217 233
Solvable Lie algebra definition      140
Solve Determining Equations      210 252 255 584 585 593 594 595 596 597 599
Sondergaard, R.      95 444 445
Soria, J.      95 430 445
Source point      13 14 127 132
Source space      188 192 240 454 570
Space of differential functions      185
Spalart, P.R.      445
Spatial similarity rules      405
Sphere drag      38 41 44 46 47 48
Sphere drag low Re      41
Spherical blast wave      375
Spreiter, J.R.      394
Squire, H.B.      339 341 362 363
Stable focus      288 417 418
Stanaway, S.K.      445
Starting vortex      330 335
State-space analysis      83 318
Steele, C.S      31
Stegeman, G.      534 550
Stegun, I.A.      262 275
Stekctee, J.A.      550
Stephani, H.      3 24 31 59 95 234 236 497 514
Stillwell, J.      xli 88 95
Stokes creeping jet      343 347
Stokes equations      30
Stokes stream function      336 337 341 343
Strain invariants      434
Stream function      60 68 74 280 323
Stream function equation      323
string variables      597
Stronge, W.J.      53 54
Structure constants of a Lie algebra      136
Structure constants of a vector space      142
Sturm — Liouville equation      260
Subalgebra      138
Subalgebra Abelian      139
Subalgebra ideal      139
Subalgebra solvable      139 157
Subgroup      10 138
Subsonic flow      386
Subsonic similarity      388
Substantial derivative      185 555
Superposition principle for linear equations      161
Supersonic flow      389
Supersonic similarity      389
Suzuki, T.      236
Symmetry analysis software      584
Symmetry and beauty      2
Symmetry continuous      12
Symmetry definition      4
Symmetry discrete      4 10
1 2 3 4
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