  In the present work the evolution of a coherent field structure of the
Sine-Gordon equation under quantum fluctuations is studied. The basic equations
are derived from the coherent state approximation to the functional
Schr\"odinger equation for the field. These equations are solved asymptotically
and numerically for three physical situations. The first is the study of the
nonlinear mechanism responsible for the quantum stability of the soliton in the
presence of low momentum fluctuations. The second considers the scattering of a
wave by the Soliton. Finally the third problem considered is the collision of
Solitons and the stability of a breather.
  It is shown that the complete integrability of the Sine-Gordon equation
precludes fusion and splitting processes in this simplified model.
  The approximate results obtained are non-perturbative in nature, and are
valid for the full nonlinear interaction in the limit of low momentum
fluctuations. It is also found that these approximate results are in good
agreement with full numerical solutions of the governing equations. This
suggests that a similar approach could be used for the baby Skyrme model, which
is not completely integrable. In this case the higher space dimensionality and
the internal degrees of freedom which prevent the integrability will be
responsable for fusion and splitting processes. This work provides a starting
point in the numerical solution of the full quantum problem of the interaction
of the field with a fluctuation.
