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Nonlinear geometric optics for short pulses. (English) Zbl 1006.35015

This paper is devoted to study pulses whose amplitudes are so large that nonlinear effects are important before diffractive effects. This scaling is called the scaling of geometric optics as opposed to diffractive geometric optics. Here for the scaling of geometric optics, an accurate asymptotic solution is constructed and the leading amplitude satisfies essentially the same nonlinear transport equation that is appropriate for slowly varying wavetrains and also the transport of jump discontinuities.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A05 Geometric optics
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