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| Stephani H., MacCallum M. (ed.) — Differential equations: Their solution using symmetries |
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| Предметный указатель |
Abelian group 50
Baecklund transformation 229
Burgers equation 222 239 243 252
Canonical equations 197
Canonical transformations 197
Cartan symmetries 117
Cole — Hopf transformation 222 230
Commutator 47
Conditional symmetry 179 219
Conformal motions 151
Conservation laws 97 117 250
Contact symmetries of ordinary differential equations 107 217
Contact symmetries of partial differential equations 204
Contact transformations of ordinary differential equations 105
Contact transformations of partial differential equations 202 204
Contact transformations, generating function 107 204
Contraction 210
Differential invariants 56 87 189
Dynamical symmetries 110 112 217 223
Einstein's field equations 158 178 240 247
Evolution equation 244
Extension of a generator 12 143
Exterior derivative 212
Exterior product 210
Finite symmetry transformations 164
First integrals 21 57 66
First integrals and symmetries 98
First integrals in involution 198
First integrals of geodesic motions 124
First order linear partial differential equations 20 149
Forms 209
Fundamental system of solutions 128 131
Galilei transformation 159 182
Generation of solutions by applying generators 44 167
Generation of solutions by finite symmetry transformations 164 246
Generator of contact transformations 106 202
Generator of Lie-Backlund transformations 226
Generator of multiple parameter point groups 14
Generator of point transformations 7 143
Generator, extension of 12
Generator, normal form of 10 61 145
Geodesic equation 123 179 196
Group 6
Group factor 83
Group of threedimensional rotations 53 75 78 79
Group, derived 52 86
Group, invariant subgroup 84
Group, realisation of 53
Group, solvable 53 86
Group, subgroup 51
Group, transitive 55
Group-invariant solutions 191
Hamilton — Jacobi equation 150 193
Hamilton — Jacobi equation, separability of 201
Heat conduction equation 157 161 165 168 175 181 214 222 229 237 242 249
Homothetic vector 127 151 179
Integrating factor 38
Invariants 56
Jacobi identity 47
Kepler problem 96 99 121 238
Kerr space-time 127
| Killing tensor 126 199
Killing vector 124 151 179 199
Korteweg — de Vries equation 159 169 182 245 252
Lie algebra 48
Lie algebra, adjoint representation 55
Lie algebra, invariants of an algebra 56
Lie algebra, realisation of an algebra 53
Lie algebra, subalgebra 51
Lie derivative 212
Lie identity 48
Lie point symmetry see Point symmetry
Lie point transformation see Point transformation
Lie — Backlund symmetry 232
Lie — Backlund transformation 225
Lie's theorem 86
Liouville equation 208
Noether symmetry 98
Orbits of a group 6 55 173
Ordinary differential equations, derivable from a Lagrangian 44 97 117
Ordinary differential equations, first order 27 36 112 128
Ordinary differential equations, linear 34 43
Ordinary differential equations, nth order 33 39 80 92
Ordinary differential equations, second order 28 36 113 216
Ordinary differential equations, second order with  59 69
Ordinary differential equations, second order with  76
Ordinary differential equations, system of second order equations 93
Ordinary differential equations, third order 88
Partial differential equations, first order 148
Partial differential equations, linear first order 20 149
Partial differential equations, second order 154
Pfaffian form 209
Poincare group 195
Poincare's lemma 212
Point symmetry of first order ordinary differential equations 27
Point symmetry of first order partial differential equations 148
Point symmetry of ordinary differential equations 17 19 22
Point symmetry of partial differential equations 141 145 147
Point symmetry of second order partial differential equations 154
Point symmetry, maximum number 36
Point transformation of ordinary differential equations 5 17
Point transformation of partial differential equations 141
Poisson bracket 197
Potential equation 155 177 191
Projective transformation 16 31 58
Prolongation of a generator 12
Recursion operator 242
Reduction of variables 170
Reduction of variables and contact symmetries 206
Reduction of variables, multiple reduction 184
Riccati equation 133
Robinson — Trautman solutions 159
Runge — Lenz vector 122
Separation of variables 193
Similarity 42
Similarity solutions 172 191 207 248
Similarity variables 171 172
Sine — Gordon equation 158 192 230
Structure constants 48
Tangency conditions 104
Vector 209
Wave equation 174 185 188 190 193 194
Wave equation, separability of 201
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