  The solution of the wave equation in the envelope approximation with temporal
corrections for a laser pulse propagating in a medium where the Kerr effect,
field ionization, and associated absorption take place, is obtained through a
first-order perturbative approach. The closed-form expressions so obtained
clarify the influence of the various terms of the equation on the laser
amplitude and on the frequency generation as a function of the retarded time.
Furthermore, they allow extracting scaling parameters which size the nonlinear
effects. The results are illustrated quantitatively on the case of a
femtosecond pulse focused in the air with typical parameters.
