  In two space dimensions and one time dimension a wave changes its shape even
in the absence of a dispersive medium. However, this anomalous dispersive
behavior in empty two-dimensional space does not occur if the wave dynamics is
described by a linear homogeneous wave equation in two space dimensions and
{\it two} time dimensions. Wave propagation in such a space can be realized in
a three-dimensional anisotropic metamaterial in which one of the space
dimensions has a negative permittivity and thus serves as an effective second
time dimension. These results lead to a fundamental understanding and new
approaches to ultrashort pulse shaping in nanostructures and metamaterials.
