We discuss laser pulse propagation with the self-similar shape in a medium with instantaneous nonlinear absorption. We consider two cases of the laser pulse propagation. First one corresponds to problem of laser-induced plasma generation in silica under action of TW laser pulse. The second one corresponds to femtosecond laser pulse propagation in medium with nanoparticles of noble metals. In both cases the mode of the self-similar shape of pulse is of interest. We discuss also a physical mechanism of non-linear acceleration or slowing-down for laser pulse propagation in a medium with nanoparticles. The last phenomena are important, in particular, for a problem of data processing of all optical method. We used analytical approach for considered problem as well as computer simulation.
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