  We adopt a variational technique to study the dynamics of perturbed
dissipative solitons, whose evolution is governed by a Ginzburg--Landau
equation (GLE). As a specific example of such solitons, we consider a
silicon-based active waveguide in which free carriers are generated through
two-photon absorption. In this case, dissipative solitons are perturbed by
physical processes such as third-order dispersion, intrapulse Raman scattering,
self-steepening, and free-carrier generation. To solve the variational problem,
we adopt the Pereira--Stenflo soliton as an ansatz since this soliton is the
exact solution of the unperturbed GLE. With this ansatz, we derive a set of six
coupled differential equations exhibiting the dynamics of various pulse
parameters. This set of equations provides considerable physical insight in the
complex behavior of perturbed dissipative solitons. Its predictions are found
to be in good agreement with direct numerical simulations of the GLE. More
specifically, the spectral and temporal shifts of the chirped soliton induced
by free carriers and intrapulse Raman scattering are predicted quite
accurately. We also provide simple analytic expressions of these shifts by
making suitable approximations. Our semi-analytic treatment is useful for
gaining physical insight into complex soliton-evolution processes.
