  We study the effect of dynamical tides associated with the excitation of
gravity waves in an interior radiative region of the central star on orbital
evolution in observed systems containing Hot Jupiters. We consider WASP-43,
Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence
(MS). For these systems there are observational estimates regarding the rate of
change of the orbital period. We also investigate Kepler-91 which contains an
evolved giant star. We adopt the formalism of Ivanov et al. for calculating the
orbital evolution.
  For the MS stars we determine expected rates of orbital evolution under
different assumptions about the amount of dissipation acting on the tides,
estimate the effect of stellar rotation for the two most rapidly rotating stars
and compare results with observations. All cases apart from possibly WASP-43
are consistent with a regime in which gravity waves are damped during their
propagation over the star. However, at present this is not definitive as
observational errors are large. We find that although it is expected to apply
to Kepler-91, linear radiative damping cannot explain this dis- sipation regime
applying to MS stars. Thus, a nonlinear mechanism may be needed.
  Kepler-91 is found to be such that the time scale for evolution of the star
is comparable to that for the orbit. This implies that significant orbital
circularisation may have occurred through tides acting on the star.
Quasi-static tides, stellar winds, hydrodynamic drag and tides acting on the
planet have likely played a minor role.
