Nonlinear geometric optics for short pulses

This paper studies the propagation of pulse-like solutions of semilmear hyperbolic equations in the lit-nit of short wavelength. The pulses are located at a wavefront Sigma:= {phi=0} where phi satisfies the eikonal equation and dphi lies on a regular sheet of the characteristic variety. The approximate solutions are u(approx)(epsilon) = U(t, x, phi(t,x)/epsilon) where U(t, x, r) is a smooth function with compact support in r. When U satisfies a familiar nonlinear transport equation from geometric optics it is proved that there is a family of exact solutions u(exact)(epsilon) such that u(approx)(epsilon) has relative error O(epsilon) as epsilon --> 0. While the transport equation is familiar, the construction of correctors and justification of the approximation are different from the analogous problems concerning the propagation of wave trains with slowly varying envelope, (C) 2002 Elsevier Science.