  We study self-similar dynamics of picosecond light pulses generating in
optical fiber amplifiers and fiber lasers with distributed parameters. A rich
variety of periodic and solitary wave solutions are derived for the governing
generalized nonlinear Schr\"{o}dinger equation with varying coefficients in the
presence of gain effect. The constraint on distributed optical fiber parameters
for the existence of these wave solutions is presented. The dynamical behaviour
of those self-similar waves is discussed in a periodic distributed
amplification system. The stability of periodic and solitary wave solutions is
also studied numerically by adding white noise. It is proved by using the
numerical split-step Fourier method that the profile of these nonlinear
self-similar waves remains unchanged during evolution.
