One-and-half-cycle pulse duration evolution in nonlinear media

Arithmetic expressions in elementary functions for center of mass movement velocity and duration evolution of initial one-and-half-cycle pulse in nonlinear medium with dispersion are obtained for the first time. It is shown that self-compression or soliton-like propagation of that pulse in the medium with positive nonlinearity doesn´t occur even if the central frequency of the pulse is in the region of medium abnormal group dispersion.