Stephani H., MacCallum M. (ed.) — Differential equations: Their solution using symmetries :: Электронная библиотека попечительского совета мехмата МГУ

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Stephani H., MacCallum M. (ed.) — Differential equations: Their solution using symmetries

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Название: Differential equations: Their solution using symmetries

Авторы: Stephani H., MacCallum M. (ed.)

Аннотация:

In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text is on how to find and use the symmetries; this is supported by many examples and more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book a valuable reference.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 260

Добавлена в каталог: 15.04.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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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