PDF《Index》

Index amplitude parameter,

136 Bernoulli's law, 43, 87, 133,

168 BottCVirasoro group,

268 Bott cocycle,

268 Euler equation,

269 GelfandCFuchs 2-cocycle,

268 Riemannian exponential map,

269 right-invariant metric,

268 bound states,

195 boundary conditions dynamic,

14 kinematic,

14 boundary layer, 32,

33 breaking wave, 241, 255,

256 plunging breaker, 241,

243 spilling breaker, 241,

243 cnoidal waves,

214 compact operator, 97,

104 complementing condition, 77, 120, 123,

124 continuum hypothesis,

5 current,

27 adverse,

69 favorable,

69 ?ood and ebb,

29 mean,

134 diffeomorphism group,

269 Lie group exponential map,

269 Riemannian exponential map,

269 right-invariant metric,

269 discriminant,

214 dispersion relation Burns condition,

71 capillary-gravity,

31 constant vorticity,

68 Gerstner's wave,

160 irrotational, 64, 65,

138 dispersive effect,

65 double spectrum,

217 drawdown,

277 elliptic regularity, 60, 61,

116 energy dissipation,

32 equation Euler, 13,

86 GelfandCLevitanCMarchenko,

206 Eulerian viewpoint,

131 Faddeev function,

190 ?nite-gap potential, 215,

216 Floquet theory,

214 ?ow-invariant set, 14,

34 Fredholm operator, 76, 77, 97, 99, 108, 110,

121 Gerstner's wave, 135,

156 global bifurcation,

105 analytic, 74, 78,

110 via generalized LerayCSchauder degree, 74, 78,

109 via LerayCSchauder degree,

105 gravity water waves, 6,

12 group speed,

282 H?lder spaces,

115 Hamiltonian system,

180 conjugate variables,

180 Hamiltonian ?ow,

186 Hamiltonian function,

184 Hamiltonian functional,

188 integrability,

186 integral of motion, 180,

189 Jacobi's identity,

181 319

320 Index Noether's theorem,

186 Poisson bracket, 181, 184,

188 symplectic map,

184 Hamiltonian vector ?eld,

184 Hardy function class, 191, 202, 204,

206 outer function,

202 HilbertCSchmidt operator,

207 homogeneity, 5,

11 homotopy, 102,

104 hydraulic head, 43, 134,

168 hyperelliptic curve,

222 homogeneous coordinates,

222 Weierstrass function,

214 irrotational ?ow,

27 isometry,

259 isospectral problem,

189 Lax pair,

199 Jost function,

189 Lagrangian viewpoint, 25, 37, 131,

156 laminar ?ow, 47,

69 LaxCMilgram, 60,

118 local bifurcation, 55, 72, 73, 79, 99, 100, 110,

114 LyapunovCSchmidt reduction, 111,

114 manifold,

182 cotangent bundle,

226 Lie derivative,

183 tangent bundle,

224 vector ?eld,

182 maximum principle,

125 Hopf, 75, 81, 86, 94, 97, 126, 134, 143,

168 Serrin, 81,

126 strong, 81C83, 91, 92, 125,

146 weak, 75, 81, 86,

126 method of stationary phase,

213 minimization problem, 49,

80 model,

237 BBM equation, 237, 247,

263 CamassaCHolm equation,

267 DegasperisCProcesi equation,

267 GreenCNaghdi equation,

246 inviscid Burgers equation,

270 Johnson equation, 248,

249 KdV equation, 165, 247,

262 linearized KdV equation,

235 moderate-amplitudelongwaves, 250, 253, 256,

263 underlying current,

273 variable depth, 272,

273 nondimensional variables,

136 norming constants, 199,

206 numerical simulation ?nite-difference method, 88,

211 spectral method,

211 PaleyCWiener theorem,

206 particle drift,

148 particle path Gerstner's wave,

157 irrotational linear theory,

139 solitary wave,

169 Stokes wave,

149 plate tectonics,

277 power series, 142,

160 pressure,

12 Gerstner's wave,

158 hydrostatic,

152 monotonicity, 153,