Physics of Waves

General Concepts on Waves > s.a. Coherence; green functions [propagator]; partial differential equations.
* Radiation vs waves: Those two concepts can usually be identified, physically, but conceptually radiation involves energy transport.
* Frequency: Measured by an observer with 4-velocity ua, ω = −ka ua.
* Wave number / vector: The spatial wave vector k and spacetime wave vector ka are the variables on which the Fourier transforms of waves depend; The vector k is perpendicular to each wave front and points in the direction in which the wave moves; For a pure-frequency wave, its magnitude k = 2π/λ.
* Power: If I = p u is the intensity vector, the power is P = S I · dA.
@ General references on waves: Georgi 93; Jonsson & Yngvason 95 [math]; AJP(01)aug [book reviews]; Nettel 08 [including solitons and chaos]; Freegarde 12 [r CP(13)]; Fitzpatrick 13; in Thorne & Blandford 15; Fleisch & Kinnaman 15 [II, student guide]; Franklin 20.
@ Related topics: Abraham-Shrauner et al JPA(06) [type-II hidden symmetries]; Orefice et al PE(15)-a1506 [exact, trajectory-based approach].
> Online resources: see MathWorld page.
> Related topics: see types of wave equations and solutions; wave phenomena [including tails in curved spacetimes, negative frequencies].

Special Techniques and Concepts for Wave Equations > s.a. green functions; velocity.
@ Initial / boundary value problem: Beyer a1211 [inequivalent formulations]; Baer & Wafo MPAG(15)-a1408 [initial-value problems on manifolds].
@ Characteristic problem: Frittelli JPA(04) [first-order reduction]; Babiuc et al CQG(14) [well-posedness].
@ Related topics: Gundlach et al CQG-a1010 [spherical harmonics decomposition in arbitrary dimensions]; > s.a. decomposition of functions; hamiltonian systems.

Types of Waves and Backgrounds > s.a. dissipative media; huygens principle; magnetism [plasmas].
* In a fluid: Acoustic waves; Surface waves; Buoyancy waves; Lamb waves (acoustic in nature, different propagation).
@ Dispersive media: Havelock 14; Kuzelev & Rukhadze 09; > s.a. dispersion.
@ Random / disordered medium: Kogan & Kaveh cm/94/PRB, FP(96); Brzezniak & Haba JPA(01)qp/00; Ramm PLA(03) [many small bodies]; Miniatura et al PRA(07)-a0704 [which-path information]; Sahlmann PRD(10)-a0911 [random lattice, dispersion relation]; Popoff et al PRL(10) + van Putten & Mosk Phy(10) + letter [transmission matrix]; Ramm a1105 [many small particles]; Willis PRS(11) [effective fields]; Godin et al WRCM(11)-a1110 [1D]; > s.a. Anderson Localization; velocity [speedup].
@ In black hole spacetimes: Dafermos & Rodnianski a0811-ln [black-hole exteriors]; Shlapentokh-Rothman AHP(15)-a1302 [Kerr spacetime, mode stability]; > s.a. kerr-ads spacetime; reissner-nordström solution; schwarzschild solution.
@ In cosmological spacetimes: Galstian et al JMP(10)-a0908 [Einstein and de Sitter spacetimes]; Battista et al IJGMP(15)-a1410 [Kasner spacetime]; Alho et al a1805 [near cosmological singularities]; > s.a. fields in FLRW backgrounds.
@ Other curved spacetimes: Pol'shin gq/98, gq/98, gq/98 [and group theory]; Grant et al CMP(09)-a0710 [singular spacetimes]; Ionescu & Klainerman CMP(09) [ill-posed problems, uniqueness results]; Falciano & Goulart CQG(12)-a1112 [new symmetry]; Harte & Drivas PRD(12)-a1202 [effects of light cone caustics]; Waldmann a1208-ln [Green functions, Cauchy problem]; > s.a. gödel solution; perturbations in general relativity.
@ Random metric fluctuations: Hu & Shiokawa PRD(98)gq/97, Shiokawa PRD(00)ht [stochastic spacetime]; Dettmann et al JPA(04) [trajectory stabilization].
@ Other backgrounds: D'Ancona & Fanelli m.AP/05 [with electromagnetic potential, dispersion]; Popov & Kovalchuk MMAS(12)-a1112 [non-uniform media]; Ingremeau a1512 [manifolds of non-positive curvature, distorted plane waves]; Dappiaggi et al LMP(19)-a1804 [static, with timelike boundary].
> Other types of waves and backgrounds: see electromagnetism; gravitational phenomena; gravitational waves; Lamb Waves; sound.

Generalizations > s.a. graph theory in physics; non-commutative theories; partial differential equations.
@ More general backgrounds: Vickers & Wilson CQG(00)gq/99 [conical spacetimes].
@ Discrete: Das CJP(10)-a0811 [covariant phase space]; Comech & Komech RJMP(11)-a1008 [well-posedness, etc]; Osharovich & Ayzenberg-Stepanenko a1108 [periodic lattices, resonant waves]; Kutsenko a1305 [on periodic lattice/graphs with defects]; > s.a. fractals in physics.