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Diffractive nonlinear geometrical optics for variational wave equations and the Einstein equations
Author(s) -
Alì Giuseppe,
Hunter John K.
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20199
Subject(s) - geometrical optics , einstein , nonlinear system , gravitational wave , diffraction , classical mechanics , wave equation , amplitude , mathematics , physics , mathematical analysis , optics , quantum mechanics
We derive an asymptotic solution of the vacuum Einstein equations that describe the propagation and diffraction of a localized, large‐amplitude, rapidly varying gravitational wave. We compare and contrast the resulting theory of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometrical optics theories for variational wave equations. © 2007 Wiley Periodicals, Inc.