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| Bluman G.W. — Similarity Methods for Differential Equations |
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| Предметный указатель |
 -variable 183
Abramowitz, M. 269
Affine transformation 2 72 112
Airy functions 217 246
Area preserving transformation 53
Asymptotic field 287 289 294
Atkinson, J. 260
Autonomous systems 132
Barenblatt, G. 182
Bauer, L. 137
Bessel functions 217
Bethe, H. 123
Bilinear group 303
Birkhoff, G. 182 198
Blasius equation 130 131 137 199
Bluman, G. 146 207 209 223 238 258 295
Bohr radius 125
boundary conditions 143 145 147 148 152 160 162 172 222 227 230 231
Boundary curve 145 152 160 162 214 222 227 230 231 238 239
Boundary layer on a wedge 198
Breiter, M. 294
Bridgman, P. 182
Brownian motion 258 271
Buckingham Pi-Theorem 183
Burgers, J. 246
Calculus of variations 116
Callegari, A. 137
Canonical coordinates 1 21 22 38 42 43 64 79 96 115 143 161
Canonical coordinates, transformation to 164—166
Cauchy — Riemann equations 53
Caughey, T. 260
Chain rule 158
Classical group 208
Cole, J. 207 209
Commutation 211
Commutator 61 212 303
Commutator table 212 250
Commutator, invariance condition using 62 91
Complex parameters, use of 219 234
Compressible flow 54 287
Confluent hypergeometric equation 215
Conformal transformation 52 113 303
Constant, definition of 188 189
Contact transformation 147
Critical solutions 120
Determining equations 145 156 282 296
Dienes, J. 260
Differential invariant 109
Diffusion equation, nonlinear 130 295
Diffusion equation, Smoluchowski's 275
Dimension matrix 183
Dimension of 183
Dimension vector 184
Dimensional analysis 3 146 166 167 174 181—199
Dimensionless quantity 183
Dimensionless variables 167—169
Dirac delta function 222
Earthworm's Christmas problem 233
Euler — Lagrange equation 117
Exceptional path 128 130 135 176 294
Exceptional solution 126
Extended group 88 103 154
Extended infinitesimal transformation 88 103 104 148 152—155 158
Extended infinitesimal transformation, symbol of 88 104
Extended transformation 84 103 152
Extended transformation, calculation for several variables 157—160
Extended transformation, invariant of 161
Extended transformation, once extended 86 152 154 159
Extended transformation, twice extended 103 152 154 155 159
Falkner — Skan equation 199
Far field 287—294
Fermi — Dirac statistics 124
First extension 152 159
Fluid flow 54 130 192—196 231—233 287
Fokker — Planck equation 258—274
Functional form of similarity solution 144 172
Fundamental dimensional unit 182
Fundamental solutions of Euler — Poisson — Darboux equation 256
Fundamental solutions of heat equation 167 179 221—230
Fundamental solutions of telegraph equation 255
Fundamental solutions of wave equation 251—255 256
Galilean transformation 210
Gas dynamics 147
General similarity solution 213
Global transformation 6 17 26 118 170
Global transformation, construction from infinitesimal 26
Global transformation, series representation of 45 81
Greub, W. 166
Group 13 15 23 157
Group, admitted by differential equation 54 59 71 89 92 94 101 107 148
Group, composition 15 16 21 23 27 31 37
Group, extended 88 103 154
Group, finding 92 148 152
Group, heat equation 206—210 303—315
Group, infinitesimals of 144
Group, multi-parameter 16 146 166 221—226 258 261 278 303
Group, one-parameter 15 23 31 77 147 149 157
Guderley, K. 286 291 293 294
Heat equation 146 147 166 206 295 303
Heat equation, fundamental solutions of 167 221—230
Heat equation, group properties of 146 147 206—210 303—315
Heat equation, nonlinear 295—302
Hermite functions 174
Hermite polynomials 216
Hodograph transformation 162
Homogeneous equation 66
Incompressible flow 54 130
Infinite-parameter group 146 282—286
Infinitesimal generator 51 88
Infinitesimal operator 203 210 260
Infinitesimal rotation 19 39 45
Infinitesimal screw 80
Infinitesimal transformation 16 25 26 31 36 144 147 150 157
Infinitesimal transformation, extended 87 148 154 158 305
Infinitesimal transformation, finding 152 155 156
Infinitesimal transformation, leaving invariant p.d.e. 145 148 152
Infinitesimal transformation, symbol of 36 39 88
Infinitesimal transformation, three variables 78
Infinitesimal transformation, uniqueness of 31
Integrating factor 61 67
Integrating factor, geometric interpretation of 67
Invariance 7 46 147 149 155 160 161 201 307
Invariance, condition 46 48 56 57 62 94 101 105 138 155 160 161 172
Invariance, criterion for a surface 84 89
Invariant boundary condition 161 222 227 230 231
Invariant boundary curve 145 161 214 222 227 230 231 238 239
Invariant coordinates 112 133 176
Invariant curve 18 20 22 47—49 83 109
Invariant differential 109
Invariant differential equation 109 111 138 161
Invariant family of curves 54 56
Invariant function 18 20 22 46 49 81
Invariant path curve 18 20 46
Invariant point 22 47 49 83
Invariant surface 83 94 151
Invariant surface condition 144 150 172 185 205 225 260 318
Invariants, finding 108 111 114 115 116
Invariants, functionally independent 173 188 262
Invariants, mutually distinct 262
Inverse Stefan problem 235—245
Jacobi's identity 211
| Jacobian 165 320
Kronecker delta symbol 158
Kummer's hypergeometric function 269
Lagerstrom, P. 197
Landau, H. 239
Langford, D. 236 239
Laplace's equation 282 291 302 303
Laurent series expansion 283
Lie algebra 211 304
Lie group 143
Lie, S. 61 146 147 207
Limiting Mach wave 291 293
Linear ordinary differential equation 112
Linear ordinary differential equation, group for 73 112
Linear second order p.d.e. 205
Linear second order p.d.e., determining equations for 156
Lorentz transformation 255
Mach lines 287
Mach number 287
Mach waves 288 291
Matschat, K. 146 147 293
Miele, A. 116
Milinazzo, F. 238
Modified Bessel functions 272
Moebius group 303
Moments 259 272 274 276 282
Momentum equation 131
Mueller, E.A. 146 147 293
Multi-parameter group 16 146 166 221—226 258 261 278 303
Navier — Stokes equations 130
Near field 291
Neuringer, J. 275
Node 293
Nonlinear diffusion equation 130 147 295—301
Nonlinear wave equation 301 302
Nonsingular solution 119
Null space 191
One-parameter group 15 23 31 77 147 149 156
Operators, extended 107
Operators, infinitesimal 203
Operators, total derivative 158
Orthogonal trajectories 64
Ovsjannikov, L.V. 146 147 248 295
Parabolic cylinder functions 215
Parameterization 25 31
Path curves 17 20 22 44 51 82 94 118 151
Path curves, interpretation of 54
Path curves, invariant 18 20 46
Path curves, one-parameter family of 17
Perspective transformation 30 73 111
Perturbation field 287
Phase plane 133 137 257
Planck's constant 124
Point transformation 101
Poisson equation 124
Poisson kernel 146 282—286
Polynomial p.d.e. 156
probability distribution 258
Probability distribution, stable 259
Projective transformation 50 53 59 84 105 210
Quantity, definition of 182
Quasilinear p.d.e's, system of first order 147
Randall, D. 293
Range space 191
Ratio of specific heats 256 287
Rayleigh flow 193—197 231—233
Reflecting boundary 259 269
Reflection, solution by 180 227
Regular solution 291
Reiss, E. 137
Repeated index 157
Riccati equation 94 108 113 176 178
Riemann function 256
Rotation group 18 35 39 41 46 57 58 64 73 88 97
Saddle point 128 293
Sanders, R. 236 239
Schlichting, H. 192
Screw transformation 78
Second extensions 152 159
Sedov, L. 182
Self-similar solutions 182
Separation of variables 218 239 242 247
Shallow membrane equations 137
Similarity 3
Similarity solutions 130 136 143 144 180 213 270
Similarity solutions, superposition of 229 230
Similarity transformation 30
Similarity transformation, variable 11 145 151 197 213 261
Similarity, curve 151
Similarity, form 130 147 151 175 181 219 261
Singular points 119 126 135 293
Singular solution 128
Smoluchowski's diffusion equation 275
Sonic line 287 288 291 293
Special path 120
Stable probability distribution 259
Stationary Markov process 258 276
Stegun, I. 269
Stochastic differential equation 258
Stream function 54 130 199
streamline 54 132
Stretching group 21 34 42 64 73 97 111 146 166 170 185 289
Stretching group, connection with dimensional analysis 170 181—199
Stretching group, examples of invariance under 117 125 132 134 200
Subalgebra 145 303 304
Subcritical solutions 120
Subgroup 145 152 296 303
Subsonic region 288
Supercritical solutions 121
Supersonic region 288
Systems of p.d.e.'s 157
Systems of p.d.e.'s, reduction of number of variables for 160 166
Szaniawski, A. 293
Telegraph equation 255
Thomas — Fermi equation 123
Three variables, infinitesimal transformation for 78
Three variables, one-parameter group in 74
Total derivative operator 158
Transformations, affine 21 72 112
Transformations, area preserving 53
Transformations, conformal 52 113 303
Transformations, contact 147
Transformations, extended 84 86 103
Transformations, global 17 26 118 170
Transformations, hodograph 172
Transformations, infinitesimal 16 25 26 31 36
Transformations, perspective 30 73 111
Transformations, point 101
Transformations, projective 50 53 59 84 105 210
Transformations, screw 78
Transformations, similarity 30
Transitional probability density distribution 258
Translation invariance 162 167 289
Translation invariance, connection with first order o.d.e.'s 4 71 97
Translation invariance, examples of 132 200
Transonic flow 286—295
Variable, definition of 188 189
Watson, G. 272
Wave equation 144 248—257
Weyl, H. 130
Zel'dovich, Y. 182
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