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Parabolic pulse generation by Raman amplification has been numerically and experimentally investigated around 1550 nm using a standard normally dispersive nonzero dispersion shifted fiber (NZ-DSF). The output pulses, characterized in intensity and phase using frequency-resolved optical gating, exhibit parabolic features in good agreement with numerical simulations based on two coupled extended nonlinear Schrödinger equations. The influence of the energy and duration of the input pulse has been studied. The ability of the parabolic pulses to propagate self-similarly during additional propagation over 800 m of NZ-DSF has also been demonstrated.