Propagation of short optical pulses in a nonlinear dispersive medium is considered without the use of slow envelope and
unidirectional propagation approximations. The existence of uniformly moving solitary solutions is predicted in the anomalous
dispersion domain. A four-parametric family of such solutions is found that contains the classical envelope soliton in the limit of
large pulse durations. In the opposite limit we get another family member, which in contrast to the envelope soliton strongly depends on nonlinearity model and represents the shortest and the most intense pulse which can propagate in a stationary manner.
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.