  The gap formation induced by a giant planet is important in the evolution of
the planet and the protoplanetary disc. We examine the gap formation by a
planet with a new formulation of one-dimensional viscous discs which takes into
account the deviation from Keplerian disc rotation due to the steep gradient of
the surface density. This formulation enables us to naturally include the
Rayleigh stable condition for the disc rotation. It is found that the
derivation from Keplerian disc rotation promotes the radial angular momentum
transfer and makes the gap shallower than in the Keplerian case. For deep gaps,
this shallowing effect becomes significant due to the Rayleigh condition. In
our model, we also take into account the propagation of the density waves
excited by the planet, which widens the range of the angular momentum
deposition to the disc. The effect of the wave propagation makes the gap wider
and shallower than the case with instantaneous wave damping. With these
shallowing effects, our one-dimensional gap model is consistent with the recent
hydrodynamic simulations.
