  We study the perturbed sine-Gordon equation $\theta_{tt}-\theta_{xx}+\sin
\theta= F(\varepsilon,x)$, where we assume that the perturbation $F$ is
analytic in $\varepsilon$ and that its derivatives with respect to
$\varepsilon$ satisfy certain bounds at $\varepsilon=0$. We construct
implicitly an, adjusted to the perturbation $F$, virtual solitary manifold,
which is invariant in the following sense: The initial value problem for the
perturbed sine-Gordon equation with an appropriate initial state on the
constructed manifold has a unique solution, which follows a trajectory on the
virtual solitary manifold. The trajectory is precisely described by two
parameters, which satisfy a specific system of ODEs.
  The approach is based on the work of Mashkin (arXiv:1705.05713), where we
constructed by an iteration scheme a virtual solitary manifold for the
perturbed sine-Gordon equation. In arXiv:1705.05713 we proved a stability
result for the perturbed sine-Gordon equation with initial data close to the
virtual solitary manifold. The employed iteration scheme produces a sequence of
virtual solitary manifolds such that the accuracy of the corresponding
stability statements increases after each iteration step, as long as the
perturbation $F$ is sufficiently often differentiable. The invariant virtual
solitary manifold constructed in this work is generated as a limit of the
virtual solitary manifolds produced by the iteration scheme.
  The method and the kind of result presented in this paper is to our knowledge
a novelty in the field of stability of solitons.
