  We predict that an ultra-cold Bose gas in an optical lattice can give rise to
a new form of condensation, namely matter X waves. These are non-spreading 3D
wave-packets which reflect the symmetry of the Laplacian with a negative
effective mass along the lattice direction, and are allowed to exist in the
absence of any trapping potential even in the limit of non-interacting atoms.
This result has also strong implications for optical propagation in periodic
structures
