Transversal perturbation effects on the self-similar pi-pulse propagation in the gain medium

The influence ofthe transversal perturbation on the self-similar monochromatic pulse, propagating in the inversed (gain) media is studied. It is found that two modes are possible: self-focusing and blowup defocusing with the forming the one-dimension pulse. The mode is determined by the value of the parameter μ, that defines the attitude of characteristic lengths ofdiffraction and dispersion.