Nonlinear geometrical optics for oscillatory wave trains with a continuous oscillatory spectrum. (English) Zbl 1034.35136

The frequency and direction of propagation of an oscillatory wave train can be read from its oscillatory spectrum. In most works on this topic the number of directions of propagation is at most countable, whereas many physical effects require a continuous infinity of directions of propagation. The purpose of the paper is to develop nonlinear geometrical optics for wave trains with continuous oscillatory spectra. This aim is accomplished by the introduction of new spaces which are Wiener algebras associated with spaces of vector-valued measures with bounded total variation. Finally, an application to Raman scattering is suggested.


35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
28B05 Vector-valued set functions, measures and integrals
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35L45 Initial value problems for first-order hyperbolic systems