Filamentation with imperfect initial beam quality

The problem of the intense femtosecond pulse with elliptical transverse distribution propagating in air is reduced to an analogous problem of a particle moving in a two-dimensional potential well using variational method. Different types of initial conditions are considered to provide direct physical insight of how the self-focusing and defocusing mechanisms can lead to long distance propagation and refocusing phenomenon. The difference between elliptical and circular transverse distribution bea