  The effect of dipolar orientation with respect to the condensate plane on the
mean-field dynamics of dipolar Bose-Einstein condensates in a pancake-shaped
confinement is discussed. The stability of a quasi-two-dimensional condensate,
with respect to the tilting angle, is found to be different from a
two-dimensional layer of dipoles, indicating the relevance of the transverse
extension while characterizing two-dimensional dipolar systems. An anisotropic
excitation spectrum exhibiting a highly tunable, rotonlike minimum can arise
entirely from the dipole-dipole interactions, by tilting the dipoles. At the
magic angle and in the absence of contact interactions, the long-wavelength
excitations are not phononlike and always unstable. The post-roton-instability
dynamics, in contrast to phonon instability, in a uniform condensate, is
featured by a transient, defect-free, stripe pattern, which eventually
undergoes local collapses, and driving the condensate back into the stable
regime can make them sustained for longer. Hopping between stripes has been
observed before it melts into a uniform state in the presence of dissipation.
Finally, we discuss a class of solutions, in which a quasi-two-dimensional
condensate is self-trapped in one direction, as well as a regime of interaction
parameters, including attractive short-range interactions, at which a
two-dimensional anisotropic soliton can be stabilized, and we show that a
chromium condensate with a relatively small number of atoms is well suited for
this.
