  We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with
scalar-scalar self-interaction in the presence of external forces as well as
damping of the form $ f(x,t) - i \mu \gamma^0 \Psi$, where both $f$ and $\Psi$
are two-component spinors. We develop an approximate variational approach using
collective coordinates (CC) for studying the time dependent response of the
solitary waves to these external forces. This approach predicts intrinsic
oscillations of the solitary waves, i.e. the amplitude, width and phase all
oscillate with the same frequency. The translational motion is also affected,
because the soliton position oscillates around a mean trajectory. We then
compare the results of the variational approximation with numerical simulations
of the NLD equation, and find a good agreement, if we take into account a
certain linear excitation with specific wavenumber that is excited together
with the intrinsic oscillations such that the momentum in a transformed NLD
equation is conserved. We also solve explicitly the CC equations of the
variational approximation in the non-relativistic regime for a homogeneous
external force and obtain excellent agreement with the numerical solution of
the CC equations.
