We investigate theoretically and experimentally the dynamics of the self-similar amplification of two optical parabolic pulses in a normally dispersive Raman amplifier. The interaction between pulses of same wavelengths creates an oscillation which further evolves into a train of dark solitons through the combined effects of non-linearity, normal dispersion and adiabatic Raman gain. In the case of pulses of different wavelengths, collisions can occur. We demonstrate that similaritons are stable against collisions: they interact during their overlap but regain their parabolic shape after collision. The collision induces a sinusoidal modulation inside the overlap region, whose frequency decreases during the interaction. Studies of the pulse spectrum evidence that similaritons interact with each other through cross phase modulation. Theoretical predictions are in good agreement with experimental results.