Coherent amplification of ultrashort solitons in doped fibers

We present the results of computer simulation of coherent amplification of solitons in doped fibers and explain the first stage of an evolution of such solitons by means of a perturbation theory applied to the inverse scattering problem in two limiting cases, noncoherent and pure coherent amplification. We show that it is possible to get adiabatic amplification of solitons. In the case of noncoherent amplification the amplitude of the solitons increases exponentially and the pulse duration decreases exponentially. In the opposite case of pure coherent amplification the amplitude of the solitons increases linearly with distance z, whereas the pulse duration displays a z(-1) dependence.