Sub-Diffractive Band-Edge Solitons in Bose-Einstein Condensates in   Periodic Potentials
  A new type of matter wave diffraction management is presented that leads to sub-diffractive soliton-like structures. The proposed management technique uses two counter-moving, identical periodic potentials (e.g. optical lattices). For suitable lattice parameters a novel type of atomic band-gap structure appears in which the effective atomic mass becomes infinite at the lowest edge of an energy band. This way normal matter-wave diffraction (proportional to the square of the atomic momentum) is replaced by fourth-order diffraction, and hence the evolution of the system becomes sub-diffractive. 
Kestutis Staliunas, Ramon Herrero and German J. de Valcarcel