A theoretical investigation on the two pulses copropagation and the red-shifted radiation generation in a photonic crystal fiber with two zero-dispersion wavelengths are presented. It is found the intensity of the red-shifted radiation components can be enhanced when the fiber is pumped with two pulses and the pulse trapping occurs. As the input peak power of the pump pulse is increased under the phenomenon of pulse trapping, the intensity of the red-shift radiation can be further enhanced. The above effects can be explained by the energy transfer from the Raman soliton to the red-shifted radi...