Stability of femtosecond solitons in optical fibres influenced by optical attenuation and bandwidth limited gain

The stability of soliton pulses which undergo the Raman self-frequency shift in the presence of bandwidth limited amplification and loss is examined. General criteria for stable propagation are given which show this behaviour is sensitive to the shape of the gain profile and loss. In particular, stability can only be achieved in a narrow spectral region of the gain.