SELF-ACTION OF ULTRASHORT PULSES IN THE SELF-SIMILAR REGIME

We study the specific features of the evolution of spatially confined pulses with a finite amplitude and a duration of several periods of wave field oscillations both analytically and numerically. The initial equation, which describes propagation of a reflectionless ultrashort pulse, is transformed to a nonautonomous modified Korteveg-de-Vries equation after passing over to self-similar variables. In this simpler equation for the self-similar function, the dynamics of the internal structure of the wave field is determined by the competition of "dispersion" and cubic nonlinearity only. The evolution of pulses in the directions of the increasing and decreasing nonlinearity is separately considered. Numerical simulation of the problem has demonstrated that: i) the energy center of the wave packet moves nonuniformly along the propagation path, ii) a dispersion shock wave consisting of a set of solitons is excited in the rear part of a pulse propagating in the direction of increasing nonlinearity in the process of the dispersion spreading, and iii) the evolution of the pulses propagating in the direction of decreasing nonlinearity is also accompanied by excitation of a breather soliton.