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**Diffractive nonlinear geometric optics with rectification.**
*(English)*
Zbl 0928.35093

This paper studies high frequency solutions of nonlinear hyperbolic equations for time scales at which diffractive effects and nonlinear effects are both present in the leading term of approximate solutions. The key innovation is the analysis of rectification effects, that is the interaction of the nonoscillatory local mean field with the rapidly oscillating fields. The main results prove that in the limit of frequency tending to infinity, the relative error in our approximate solutions tends to zero. One of our main conclusions is that for oscillatory fields associated with wave vectors on curved parts of the characteristic variety, the interaction is negligible to leading order. For wave vectors on flat parts of the variety, the interaction is spelled out in detail.

Reviewer: J.Rauch (Ann Arbor)

### MSC:

35L60 | First-order nonlinear hyperbolic equations |

78A05 | Geometric optics |

35C20 | Asymptotic expansions of solutions to PDEs |