Propagation of optical solitons in fiber amplifiers is discussed by considering a model that includes gain dispersion, intrapulse stimulated Raman scattering (ISRS) and two-photon absorption. The numerical results show that the amplification of optical solitons is unstable in the anomalous dispersion regime. The soliton pulses split into several subpulses symmetrically because of gain dispersion while ISRS results in soliton pulses split asymmetrically. An interplay between the effects of gain dispersion and ISRS can lead to novel temporal and spectral features. Bandwidth limited amplification of soliton pulses can suppress the self-frequency shift induced by ISRS. Propagation of chirped soliton pulses are also analyzed.