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


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 380

Добавлена в каталог: 19.04.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\check{C}$erenkov radiation      53 60
$\textit{k}$th Riemann invariant      87 88
$\textit{k}$th simple wave      87 88
Acoustics, geometrical      159 ff
Adiabatic, curve      329
Adiabatic, gas      58
Adiabatic, law for water waves      64
Adiabatic, reversible fluid      170
Alfven      6
Alfven, number      244 295
Alfven, rays      185 186 193 201
Alfven, shock $(180^{o})$      264
Alfven, shock and slow shock      268 269 270
Alfven, speed      173
Alfven, wave      176 200 261
Alfven, wave in incompressible fluid      175 200
Alfven, waves, outgoing      222 346
Aligned-field flow      293 354
Analytic initial data      10 13 27 40
Axis, optical      56
Basis      325
Bernoulli’s equation      300 354
Bernoulli’s theorem      294 300
Bilinear form      323
Biorthogonal set      325
Body force, Lorentz      168
Boundary conditions on piston      260 ff
Boundary conditions on spacelike arc      99 100
Bounded derivative and Lipschitz continuity      27
Branches of a shock      229 231 311 336
Cauchy, problem      13 40
Cauchy, sequence      20
Cavitation in pure gas wave      269
Cavitation in slow rarefaction      209 210 260 262 266 271
Centred rarefaction wave      134 345
Centred rarefaction wave, fast      264
Centred rarefaction wave, slow      262
Centred simple wave      73 91
Characteristic equations      7 12 35 38
Characteristic equations for a transmission line      83
Characteristic equations for gas dynamics      59
Characteristic equations for general non-linear equation      14
Characteristic equations for magnetohydrodynamics      172
Characteristic equations for non-isentropic flow      59
Characteristic equations for shallow water      81
Characteristic equations for supersonic flow      79
Characteristics as wavefront      28
Characteristics, $C^{\pm}$      67 ff 79 81 300
Characteristics, bounding constant state      88
Characteristics, curves      7 12 66 89 142
Characteristics, curvilinear coordinate net      199
Characteristics, determinant      34 324
Characteristics, direction      14 36 143
Characteristics, field      89 98 68 70 72 79 304 307
Characteristics, hypercone      46 52
Characteristics, manifold      34 65
Characteristics, parametisation      67 68
Characteristics, rays      184
Characteristics, surface      36
Charge conservation law      48
Collision of shocks      141 292
Completely exceptional system      90 106 108
Compressible flow      92
Compression, fast and slow waves      209
Compression, maximum      210 229 242 270
Compressive shock      328
Condition, (C)      227 333
Condition, (R)      227
Confinement of plasma      319
Conformability of matrices      321 ff
Conical refraction      194
Conservation laws      57 111
Conservation laws, differential form      112
Conservation laws, energy      57 169 217
Conservation laws, generalised      116
Conservation laws, generalised, integral form      111
Conservation laws, generalised, magnetohydrodynamic      214 ff
Conservation laws, generalised, mass, momentum and energy      57
Conservation laws, generalised, symmetric hyperbolic      152
Conservation of magnetic flux      225
Constant state line      87
Constitutive equations      49 167
Contact, discontinuity      136 160 218 249 252 255
Contact, layer      213
Contact, surface      60 109 176 289 338
Contact, transformation      347 ff
Continuity, equation      169
Continuity, Lipschitz      27 39 100 103
Contraction mapping      20 21 99
Convergence in the mean      121
Convergence, strong      121 123
Convergence, weak      121
Courant, method of      142 ff
Critical, point      106 109
Critical, speed      304 307
Critical, time $t_{c}$      100 104 107
Crystal optics      53 185
Cusp      72
Derivative, directional      10 33 66 81 146
Derivative, generalised      118
Determinant, characteristic      34 324
Determined system      29
Diadic product      58
Diagonalising matrix      96
Difference quotients, forward and backward      143
Differentiation of a matrix      322 323
Differentiation, along a ray      154
Directions, characteristic      14 36 143
Discontinuity, development and propagation of      90 100
Discontinuity, exceptional      128 129 134 250 345
Discontinuity, propagation of weak      149 ff
Discontinuity, spatial      47 52 61 186 293
Discontinuity, static case      317 ff
Discontinuity, weak      260
Displacement vector, electric      168
Divergence condition, variational      191
Domain of dependence      9 15 99 142 144
Domain of dependence, existence and uniqueness      21 24
Double layer shock      258
Eigenvalues of a matrix      324
Eigenvalues redundant      38
Eigenvalues, multiplicity k      326
Eigenvectors of a matrix      324
Eigenvectors, generalised left and right      326
Eigenvectors, jth right      325
Eigenvectors, left      66 75 325
Eigenvectors, right      87 92 325
Electromagnetic, field equations in a conductor      168
Electromagnetic, polarised waves      55
Electromagnetic, scalar potential      50
Electromagnetic, transverse nature of waves      49
Electromagnetic, vector potential      50 196
Elliptic equation      6
Elliptic-hyperbolic, magnetohydrodynamic flow      187 311
Energy, internal      58 169
Energy, total      57 169
Entropy wave, degenerate      177
Entropy, condition      115 122
Entropy, disturbance, matrix representation      341
Entropy, increase across shock      328
Entropy, jump in fast shock      230
Entropy, jump in slow shock      239
Entropy, simple wave      203
Envelope, of discontinuities      72
Equation, of mixed type      6
Equi-pressure surfaces      318 319
Evolutionary condition      125 ff
Evolutionary condition and fast shocks      231
Evolutionary condition and gas shocks      137 ff
Evolutionary condition and slow shocks      234 ff
Evolutionary condition in magnetohydrodynamics      218 220 256 345
Evolutionary, discontinuities      128
Evolutionary, weakly      258
Exceptional      345
Exceptional case      100 107 110 213
Exceptional system      90 106
Expansion ratio      156 158
Expansion ratio in magnetohydrodynamics      194
Expansion wave      73
Expansion wave and initial discontinuity      74
Fast disturbance, matrix representation      340
Fast shock      217 218 219 224 227 259 264 269 313 335
Fast shock and Alfven shock      220
Fast shock, $90^{o}$ limit      247 ff
Fast shock, dependence on parameters      232 233
Fast shock, type (1)      229 240 335
Fast shock, type (2)      229 241 335
Fast wave      173 183 184 205 208 295 304
Fast wave, simple      203 210 212
Field, divergence free      112
Field, divergence free, kth      89
Finite difference equations      143
Finite difference equations, along characteristics      146
Finite discontinuity, propagation      90 ff
First order quasi-linear systems      24 ff
First order quasi-linear systems and Cauchy problem      40
Fixed point theorem      21
Flow, aligned-field      354
Flow, homentropic      299
Flow, incompressible magnetohydrodynamic      198
Flow, isentropic      71 91
Flow, isentropic and irrotational plane      354
Flow, non-isentropic      58 92
Flow, past a conducting convex wall      309
Flow, past a sharp corner      297 312
Flow, steady supersonic      76
Fluid motion equations      169
Fluid pressure      176
Flux, magnetic      225
Flux, scalar      111
Free surface      62
Fresnel equation      54
Friedrichs diagram      181 ff 186
Frozen-in condition      197 198 210
Functional, linear      117
Gas, basic physical properties      220 327
Gas, dynamic conservation laws      135
Gas, shock      136 244 258 265 334
Gas, simple waves      334
Gaussian units      167
Genuinely non-linear      91 121
Goursat problem      17
Hamilton — Jacobi equation      42 184
Hamiltonian      42 46 184 193
Heat, conduction coefficient      58
Heat, equation      58
Heat, flow vector      169
Hodograph, plane      303 352
Hodograph, transformation      80 299 302 352
Homentropic flow      299
Homogeneous hyperbolic equations      66 79
Hugoniot function      217 327
Hydrodynamic contact discontinuity      138
Hydrodynamics, basic equations      57
Hydromagnetic, equations in matrix form      339 ff
Hydromagnetic, shock relations      334 ff
Hydromagnetic, simple waves      337
Hydromagnetic, stability      320
Hydrostatic pressure      63
Hyperbolic equations      6 37 66
Hyperbolic equations, normal form      7 17 19
Hyperbolic equations, symmetric      153
Hyperbolic, totally      37 38 94
Hyperbolic, ultra      37 38
Hyperbolic-fast      315 ff
Hyperbolic-slow      315 ff
Hyperplane      33
Identity matrix      322
Incompressible, fluid      61
Incompressible, magnetohydrodynamic flow      198
Indefinite quadratic form      324
Indeterminacy of normal derivative      34
Initial, curve      16
Initial, data      9
Initial, interval and boundary values      98
Initial, point      208
Initial, value problem      24
Integral, curves for magnetohydrodynamic flow      205 206
Integral, equation, solution by iteration      21
Intermediate discontinuity      129
Intersection of characteristics      70 72 103
Invariant, measure      196
Invariant, transformation      218
Inverse matrix      322
Involutory transformation      349
Isentropic, flow      71 91 105 294 354
Isentropic, spherical flow      108
Jacobian      67 101 352
Jacobi’s theorem      155
Joule heating      244
Jump conditions and evolutionary condition      226
Jump conditions, across wavefront      4 5 102 107
Jump in variational quantities      151
Jump, discontinuity      113
Klein bottle      319
Kronecker delta      46
Lax’s condition      125 128
Lax’s condition and gas shock      138
Left eigenvector      66 75 325
Legendre transform      311 349 351
Legendre transform and potential flow      352
Limit, $0^{o}$ fast shock      240
Limit, $0^{o}$ slow shock      247
Limit, $90^{o}$ fast shock      247
Limit, $90^{o}$ slow shock      247
Limit, shocks      238 ff 258
Limit, strong      121 123
Limit, weak      121
Limiting operation in $\mathfrak{L}$      102
Linear equations      3 29 32
Linearly independent eigenvectors      325
Lipschitz continuity      27 39 100 103
Lorentz, body force      168
Lorentz, transformation      51
Lundquist equations      171
Lundquist equations and steady spatial discontinuities      317 ff
Lundquist equations, isentropic flow      189
Lundquist equations, linearised one-dimensional      221 342
Mach, angle      78
Mach, fast and slow wave      295 297 302 305 307
Mach, lines      77
Mach, number      77 295
Mach, wave      60 186 293 297
Magnetic, lines of force and properties      195 ff
Magnetic, pressure      176 204 210 297 319
Magnetic, Riemann invariant      207
Magnetic, stress tensor      169
Magnetic, surfaces      318
Magnetoacoustic waves      174 222 223 345
Magnetoacoustic waves and Alfven shocks      281
Magnetoacoustic waves, combination and interaction      280 ff
Magnetoacoustic waves, shock      261 345
Magnetoacoustic waves, simple      203 204
Magnetohydrodynamic, basic assumptions      167
Magnetohydrodynamic, characteristic equations      172
Magnetohydrodynamic, conservation laws      214 ff
Magnetohydrodynamic, elliptic-hyperbolic flow      187 311
Magnetohydrodynamic, evolutionary conditions      218 220 256 345
Magnetohydrodynamic, incompressible flow      198
Magnetohydrodynamic, mechanical relations      216 219 226
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