  We study the classical dynamics of the Abelian-Higgs model in (1+1)
space-time dimensions bf for the case of strongly broken gauge symmetry. In
this limit the wells of the potential are almost harmonic and sufficiently
deep, presenting a scenario far from the associated critical point. Using a
multiscale perturbation expansion, the equations of motion for the fields are
reduced to a system of coupled nonlinear Schrodinger equations (CNLS). Exact
solutions of the latter are used to obtain approximate analytical solutions for
the full dynamics of both the gauge and Higgs field in the form of oscillons
and oscillating kinks. Numerical simulations of the exact dynamics verify the
validity of these solutions. We explore their persistence for a wide range of
the model's single parameter which is the ratio of the Higgs mass to the gauge
field mass . We show that only oscillons oscillating symmetrically with respect
to the "classical vacuum", for both the gauge and the Higgs field, are long
lived. Furthermore plane waves and oscillating kinks are shown to decay into
oscillon- like patterns, due to the modulation instability mechanism.
