The evolution of self-similar parabolic pulses is demonstrated by designing a parabolic index dispersion decreasing fiber amplifier with normal dispersion (ND-DDF amplifier), with inclusion of the variation of nonlinear factor (gamma) with distance. The pulse transmission is extensively studied for the proposed ND-DDF in presence of external gain as well as virtual gain induced by its dispersion profile. The output power resembles with a perfect parabolic shape giving rise to self-similar pulses with minimum misfit les 0.003. In view of practical aspects of fabrication we also obtain several equivalent staircase profiles, whose performances are shown to be very close to that of the proposed ND-DDF.