  We demonstrate that light is subject to anomalous (i.e., negative)
diffraction when propagating in the presence of hyperbolic dispersion. We show
that light propagation in hyperbolic media resembles the dynamics of a quantum
particle of negative mass moving in a two-dimensional potential. The negative
effective mass implies time reversal if the medium is homogeneous. Such
property paves the way to diffraction compensation, spatial analogue of
dispersion compensating fibers in the temporal domain. At variance with
materials exhibiting standard elliptic dispersion, in inhomogeneous hyperbolic
materials light waves are pulled towards regions with a lower refractive index.
In the presence of a Kerr-like optical response, bright (dark) solitons are
supported by a negative (positive) nonlinearity.
