  We propose and study a continuum model for the dynamics of amorphizable
surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and
oblique incidence. After considering the current limitations of more standard
descriptions in which a single evolution equation is posed for the surface
height, we overcome (some of) them by explicitly formulating the dynamics of
the species that transport along the surface, and by coupling it to that of the
surface height proper. In this we follow recent proposals inspired by
``hydrodynamic'' descriptions of pattern formation in aeolian sand dunes and
ion-sputtered systems. From this enlarged model, and by exploiting the
time-scale separation among various dynamical processes in the system, we
derive a single height equation in which coefficients can be related to
experimental parameters. This equation generalizes those obtained by previous
continuum models and is able to account for many experimental features of
pattern formation by IBS at oblique incidence, such as the evolution of the
irradiation-induced amorphous layer, transverse ripple motion with non-uniform
velocity, ripple coarsening, onset of kinetic roughening and other.
Additionally, the dynamics of the full two-field model is compared with that of
the effective interface equation.
