  We study the dynamics of the sine-Gordon model after a quantum quench into
the attractive regime, where the spectrum consists of solitons, antisolitons
and breathers. In particular, we analyse the time-dependent expectation value
of the vertex operator, $\exp\left({\rm i}\beta\Phi/2\right)$, starting from an
initial state in the "squeezed state form" corresponding to integrable boundary
conditions. Using an expansion in terms of exact form factors, we compute
analytically the leading contributions to this expectation value at late times.
We show that form factors containing breathers only contribute to the late-time
dynamics if the initial state exhibits zero-momentum breather states. The
leading terms at late times exponentially decay, and we compute the different
decay rates. In addition, the late-time contributions from the zero-momentum
breathers display oscillatory behaviour, with the oscillation frequency given
by the breather mass renormalised by interaction effects. Using our result, we
compute the low-energy contributions to the power spectrum of the vertex
operator. The oscillatory terms in the expectation value are shown to produce
smooth peaks in the power spectrum located near the values of the bare breather
masses.
