  A semianalytic theory for the pulse dynamics in similariton amplifiers and
lasers is presented, based on a model pulse with adaptive shape. By changing a
single parameter, this test function can be continuously tweaked between a pure
Gaussian and a pure parabolic profile and can even represent sech-like pulses,
the shape of a soliton. This approach allows us to describe the pulse evolution
in the self-similar and other regimes of optical propagation. Employing the
method of moments, the evolution equations for the characteristic pulse
parameters are derived from the governing nonlinear Schr\"odinger or
Ginzburg-Landau equation. Due to its greatly reduced complexity, this
description allows for extensive parameter optimization, and can aid intuitive
understanding of the dynamics. As an application of this approach, we model a
soliton-similariton laser and validate the results against numerical
simulations. This constitutes a semianalytic model of the soliton-similariton
laser. Due to the versatility of the model pulse, it can also prove useful in
other application areas.
