Analysis of propagation of Raman-pump-supported solitons in a nonlinear-optical fiber

Propagation of a soliton in a lossy fiber with Raman energy transfer from a continuous pump wave is analyzed under the assumptions that the soliton amplitude is much larger than the pump wave and that the soliton is sufficiently narrow. It is demonstrated that the Raman amplification mechanism gives rise to a continuous downshift of the central frequency of the soliton in agreement with recent numerical simulations.