Femtosecond pulse propagation in air: Variational analysis

We use a variational method to study the phenomenon of intense femtosecond pulse propagation in air. This method allows us to obtain a semianalytical solution to the problem in which a wide range of initial conditions can be studied. In addition, it provides a simple physical interpertation, where the problem is reduced to an analogous problem of a particle moving in a potential well. Different types of possible solutions are considered, with focus upon the main physical interpretations. The results recapture at least qualitatively some of the major experimental observations, and previous numerical simulations.