Diffractive nonlinear geometric optics with rectification

This paper studies high frequency solutions of nonlinear hyperbolic equatio ns for time scales at which diffractive effects and nonlinear effects are b oth present in the leading term of approximate solutions. The key innovatio n is the analysis of rectification effects, that is the interaction of the nonoscillatory local mean field with the rapidly oscillating fields. The ma in results prove that in the limit of frequency tending to infinity, the re lative error in our approximate solutions tends to zero. One of our main co nclusions is that for oscillatory fields associated with wave vectors on cu rved parts of the characteristic variety, the interaction is negligible to leading order. For wave vectors on hat parts of the variety, the interactio n is spelled out in detail.