362 Index
ray cone, 77, 78
ray tracing algorithms, 166
rays, 144–145
and conormal waves, xviii
spread of, 25
transport along, 2, 23, 161–177,
285–289
tube of, 26, 34, 100, 147, 148, 288
rectilinear propagation, xvi, 20–27
reflection
coefficient of, 32, 35, 36
law of, xvi, 28
operator, 30
total, 42
refraction, Snell’s law, xvi, 36–42
resonance, xviii
collinear, 341
examples of, 291–302, 317–332
introduction to, 291–294
quadratic, definition, 341
quasilinear, 302–314, 327–332
relation, 292
relations for Euler equations, 341–342
semilinear, 291–302, 314–315,
321–327
omer, xvi
Schauder’s lemma, 217–222
Schr¨ odinger’s equation, 149–151
self phase modulation, 287, 288
semiclassical limit of quantum
mechanics, 278
semisimple eigenvalue, 117
short wavelength asymptotic analysis,
xvi
singularities
(microlocal) of piecewise smooth
functions, 140
and the method of characteristics,
10–11
for progressing waves, 12–16
propagation for piecewise smooth
waves, 10–11, 194
propagation global in time, 192–195
propagation local in time, 188–191
propagation of, xiv, xviii
propagation of and stabilization,
195–205
slowly varying envelope approximation,
287
small divisor, 310–313
hypothesis, 312, 318
for Euler equations, 339
smooth characteristic variety
hypothesis, 163–178, 286–289
smooth points, of the characteristic
variety, 76–78
Snell’s law, see refraction
Sobolev embedding, 216, 220
space like, 146
spectral projection, 117
spectrum
of a periodic function, 309
of F (V ), 315
of principal profile, 309
stability
Hadamard’s notion of, 43
theorem, quasilinear, 314
theorem, semilinear, 283
stationary phase, 210
stationary phase inequality, 120–122
stationary point, nondegenerate, 120
stratification theorem, 76, 94, 99
Strichartz inequalities, xii, 111–117,
251–257
three wave interaction
infinite system, 337
ode, 298–302, 330–332, 336
pde, 294–298, 322–327
resonance of order three, 341
time of nonlinear interaction
quasilinear, 303
semilinear, 262
time-like, 146
cone, 64–71
transport equation, 144, 146
wave
acoustic, xiv, 341
conormal, xviii, 16, 194
plane, 14, 33–34, 71–79, 150
progressing, 12–16
shock, xv, 12
short pulse, xvi
spherical, 32, 171–173
vorticity, 341
wave packet, xiv, 1, 22–28, 34–36, 142
wave train, 1, 291
wave number, good and bad, 93–96
wavefront set, 136–140, 186–195,
201–204
Wiener algebra, 96
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