  We investigate the dynamics of the sine-Gordon solitons perturbed by
spatiotemporal external forces. We prove the existence of internal (shape)
modes of sine-Gordon solitons when they are in the presence of inhomogeneous
space-dependent external forces, provided some conditions (for these forces)
hold. Additional periodic time-dependent forces can sustain oscillations of the
soliton width. We show that, in some cases, the internal mode even can become
unstable, causing the soliton to decay in an antisoliton and two solitons. In
general, in the presence of spatiotemporal forces the soliton behaves as a
deformable (non-rigid) object. A soliton moving in an array of inhomogeneities
can also present sustained oscillations of its width. There are very important
phenomena (like the soliton-antisoliton collisions) where the existence of
internal modes plays a crucial role.
