The nonlinear Schrödinger equation based on the Taylor approximation of
the material dispersion can become invalid for ultrashort and few-cycle
optical pulses. Instead, we use a rational fit to the dispersion function
such that the resonances are naturally accounted for. This approach allows us
to derive a simple non-envelope model for short pulses propagating in one
spatial dimension. This model is further investigated numerically and
analytically.
