  We describe similariton pulse propagation in double-doped optical fibers with
the aid of self-similarity analysis of the cubic-quintic nonlinear
Schr\"odinger equation with varying dispersion, nonlinearity, gain or
absorption, and nonlinear gain. Exact similariton pulses that can propagate
self similarly subject to simple scaling rules of this model have been found
using a fractional transform. By appropriately tailoring the dispersion profile
and nonlinearity, the condition for optimal pulse compression has been
obtained. Also, nonlinear chirping of the trigonometric solution has been
demonstrated.
