Jeffrey A., Taniuti T. — Mathematics in Science and Engineering: volume 9. Non-linear wave propagation :: Электронная библиотека попечительского совета мехмата МГУ

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Jeffrey A., Taniuti T. — Mathematics in Science and Engineering: volume 9. Non-linear wave propagation

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Название: Mathematics in Science and Engineering: volume 9. Non-linear wave propagation

Авторы: Jeffrey A., Taniuti T.

Аннотация:

This book represents an attempt to present the basic mathematics of non-linear wave propagation in a systematic manner and to display it against the background of modern theoretical physics. In Part I of the book, basic ideas are developed and examples from
several branches of physics are used to illustrate the application of these ideas in diverse situations. It is hoped that in this manner the power of these methods may be indicated more directly and application to other branches encouraged. Part II of the book is a study of those topics of magnetohydrodynamics which permit exact analysis making use of these methods.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1964

Количество страниц: 380

Добавлена в каталог: 19.04.2011

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Предметный указатель

Magnetohydrodynamic, orthogonality relation      192
Magnetohydrodynamic, piston problem      259 ff
Magnetohydrodynamic, Rankine - Hugoniot relation      217
Magnetohydrodynamic, reducible flow      188 201 202 253
Magnetohydrodynamic, Riemann invariant      199 207 208 259 299 303
Magnetohydrodynamic, Riemann problem      276 ff
Magnetohydrodynamic, space-time scale      167
Magnetohydrodynamic, steady flow      293
Magnetohydrodynamic, symmetric hyperbolic equations      173
Magnetohydrodynamic, waves      174
Manifold      65
Manifold, normal to      33
Mapping, $C^{\pm}$ and $\Gamma^{\pm}$ characteristics      69
Matrices, basic properties      321 ff
Matrices, conformability of      322
Matrices, diagonalising      96
Matrices, differentiation of      322 323
Matrices, eigenvectors and eigenvalues of      324
Matrices, product of      322
Matrices, sum of      321
Matrices, transpose of      152 322
Maxwell equations      48
Mechanical pressure      210
Mechanical relations in gas dynamics      136
Mechanical relations in magnetohydrodynamics      216 219 226
Metric space, complete      20
Mixed boundary and initial value problem      17 94
Momentum equation      169
Navier — Stokes equation      62
Negative branch shock      229 231 331 333 336
Net points      142
Node of integral curve      206
Non-characteristic curve      13
Non-compressive wave      175
Non-evolutionary shocks      258
Non-isentropic flow      58 92
Non-isentropic flow, generalised Riemann invariants      93
Non-linear string      74
Non-magnetic shock      242
Non-singular matrix      322
Non-uniqueness      119 ff
Normal velocity      42 43 50
Normal velocity surface      44 46 178
Null matrix      322
Oblique shock waves      311
Ohm’s Law      168
One-parameter family      131 149
Optical axis      56
Optics, geometrical      40
Orthogonal complement      89
Orthogonality of $C^{\pm}$ and $\Gamma^{\pm}$ characteristics      79
Orthogonality, relation      153 157 161
Orthogonality, relation in magnetohydrodynamics      192
Outgoing waves      125 ff 222 244
Parabolic equation      6
Parametric representation of $C^{\pm}$ characteristics      68
Particle trajectories and characteristic rays      185
Perfect gas      58
Perpendicular shock      247
Piston, boundary conditions in magnetohydrodynamics      260
Piston, motion in a tube      73
Piston, problem      140
Piston, problem in magnetohydrodynamics      259 ff
Plane flow, reducible      299
Plane, interaction problem      278 ff
Plane, shock      215
Plane, wave      200
Plastic deformation      76
Point transformation      347
Polarised electro-magnetic wave      55
Positive definite      31 323 324
Potential, functions      351
Potential, vector      50 196
Power series solution      10 ff
Pressure, magnetic      176 204 210 297 319
Pressure, total      176 319
Propagation of discontinuities along characteristics      100 ff
Propagation of weak hydromagnetic discontinuities      189 ff
Pure gas, limits      243 ff
Pure gas, rarefaction wave      269
Pure gas, shock      240 242
Pure gas, wave      212
Purely transverse magnetohydrodynamic flow      201
Quadratic form      323 324
Quadratic Hamiltonian      45
Quasi-linear equations      3 29 32
Range of influence      9
Rankine-Hugoniot relation      114 120 139 241 248 327
Rankine-Hugoniot relation and entropy condition      124
Rankine-Hugoniot relation in magnetohydrodynamics      217
Rankine-Hugoniot relation, generalised      114 116 119
Rankine-Hugoniot relation, variational form      151
Rarefaction wave, centred      134 262 345
Rarefaction wave, complete      209 210
Rarefaction wave, fast and slow      209 268
Rarefaction wave, maximum      210 268 269
Rarefaction wave, slow      266 ff
Rarefaction, fast      269
Rarefaction, maximum      210 268
Ray      41 42 154
Ray, fast      185 186
Ray, optics      40
Ray, propagation of weak discontinuity      153
Ray, slow      185 186
Ray, transverse      185
Ray, tube      157
Ray, velocity      42 43 50
Reality condition (R)      227
Reducible equation      79
Region $\mathfrak{L}$       102
Region $\mathfrak{R}$       106
Resolution of an initial discontinuity      276 ff
Riemann initial value problem      134 135
Riemann invariant      69 72 75 85 105
Riemann invariant in magnetohydrodynamics      199 207 208 259 299 303
Riemann invariant, change across k-shock      133
Riemann invariant, generalised $\textit{k}$ th      85 87 88 93
Riemann invariant, magnetic      207
Riemann invariant, non-existence of direct generalisation      86
Riemann’s problem in magnetohydrodynamics      276 ff
Right eigenvector      87 92 325
Rotational interaction problem      289 ff
Secular equation in crystal optics      53
Semi-linear equation      3 32
Shear flow discontinuity      60 253 275
Shock      216
Shock and evolutionary condition      226 ff
Shock, development of      105
Shock, double layer switch-on switch-off      258
Shock, entropy increase across      328
Shock, fast types (1), (2)      229 230 331 332

Shock, fitting      148
Shock, general relations      130 ff
Shock, genuine      128 222
Shock, k-genuine      131
Shock, perpendicular      247
Shock, polar      311
Shock, slow types (1), (2)      235 331 332
Shock, speed and characteristic speeds      132
Shock, tube      140
Shock, wave      114 115
Simple wave, adjacent to constant state      71 90
Simple wave, centred      73 91 132
Simple wave, gas      334
Simple wave, generalised      86
Simple wave, hydromagnetic one-dimeneional      202 ff 337 345
Simple wave, hydromagnetic three-dimensional      199 200
Singly simple wave      201
Skew-symmetric matrix      322
Slow disturbance, matrix representation      340
Slow shock      217 218 219 224 234 260 265 270 314 336
Slow shock, $0^{o}$ limit      247
Slow shock, dependence on parameters      237 ff
Slow shock, dependence on parameters, $90^{o}$ limit      249
Slow shock, dependence on parameters, type (1)      235
Slow shock, dependence on parameters, type (2)      235
Slow simple wave      203 210 212
Slow wave      173 182 184 186 205 208 295 304 340
Slow wave, forward facing      188
Slow wave, front emerging from sphere      183
Solitary wave      28
Solution, basic      148 153 190 191
Solution, generalised      28
Solution, genuine      119
Solution, physically relevant      124
Sound wave      60
Space-like      15 36 94 95
Space-time scale in magnetohydrodynamics      167
Spatial discontinuity      186 187 293
Stability, hydromagnetic      320
Steady      76 77
Steady-state condition      150 190 191
Stress tensor, hydrodynamic      57 169
String, non-linear      74
Sub-fast flow      223 231
Sub-slow flow      223 236
Subsonic      96
Summation convention      34
Super-Alfvenic flow      242
Super-fast flow      223 231
Super-slow flow      223 236
Supersonic flow, characteristics      79
Surfaces of normal velocity      179
Switch-off shock      238 247 257
Switch-off simple wave      209 212
Switch-on shock      238 240 241 242 257 275 337
Switch-on simple wave      212
Switch-on slow wave      272
Sylvester’s law of inertia      324
Symmetric, difference quotients      148
Symmetric, hyperbolic equations      153
Symmetric, hyperbolic equations of magnetohydrodynamics      173
Symmetric, matrix      322
Symmetry preserving transformation      31
Tangent hyperplane      36
Test function      117
thermal conductivity      58 169
Thermodynamic equation      169
Thermodynamical relation      220 328
Time-like      17 36 94 95
Torus      319
Torus, long and short paths      319
Torus, twisted      320
Totally hyperbolic      94
transform      320
Transform, involutary      349
Transform, Legendre      349 ff
Transform, point and contact      347 ff
Transmission line, characteristics      81
Transmission line, electric      81
Transverse, disturbance, hydromagnetic wave      109 338
Transverse, disturbance, magnetic field jump      224
Transverse, disturbance, matrix representation      341
Transverse, disturbance, shock      218 249 260 338
Transverse, disturbance, simple wave      203 212
Transverse, disturbance, speed, variation with direction      178
Transverse, disturbance, velocity jump in magnetohydrodynamics      227 241
Transverse, disturbance, wave      173 175 181 184 217 223 341
Transverse, disturbance, wave, exceptional nature      213 345
Tricomi equation      6
Types (1), (2) shocks      229 ff
Undistorted wave propagation      84
Uniqueness of domain of dependence      24
Unit matrix      322
Variation of scale factor along a ray      154 156 159
Variational equations      151
Variations      150
Vector, potential      50 196
Vector, row and column      321
Velocity profile, steepening of      105
Viscosity, coefficient      58
Viscosity, method      123
Viscosity, term in parabolic equation      123
Viscosity, term in weak solutions      122 123
Wave      3
Wave front      4 40 43 44
Wave front, diagram      177 ff
Wave front, discontinuity jump across      5 102 107
Wave front, normal      37 38
Wave front, propagation of discontinuities along      100 ff
Wave front, shock      239
Wave front, speed relative to fluid      172
Wave front, velocity      38
Wave, $\textit{k}$ th simple      87 88
Wave, Alfven      176
Wave, centred simple      73
Wave, entropy      173
Wave, expansion      73
Wave, fast      173
Wave, magnetohydrodynamic      174
Wave, plane      200
Wave, shallow water      63 80
Wave, simple      71 72 90 334
Wave, slow      173
Wave, sound      60
Wave, transverse      173
Wave, zero phase      129
Weak discontinuity      260
Weak discontinuity in steady flows      293 ff
Weak discontinuity, hydromagnetic      189 ff
Weak discontinuity, selection of physically relevant solution      122
Weak discontinuity, weak solution      119
Weakly evolutionary      258 261

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