  We derive various approximations for the solutions of nonlinear hyperbolic
systems with fastly oscillating initial data. We first provide error estimates
for the so-called slowly varying envelope, full dispersion, and Schr\"odinger
approximations in a Wiener algebra; this functional framework allows us to give
precise conditions on the validity of these models; we give in particular a
rigorous proof of the ``practical rule'' which serves as a criterion for the
use of the slowly varying envelope approximation (SVEA). We also discuss the
extension of these models to short pulses and more generally to large spectrum
waves, such as chirped pulses. We then derive and justify rigorously a modified
Schr\"odinger equation with improved frequency dispersion. Numerical
computations are then presented, which confirm the theoretical predictions.
