  The modulational instability and discrete matter wave solitons in dipolar
BEC, loaded into a deep optical lattice, are investigated analytically and
numerically. The process of modulational instability of nonlinear plane matter
waves in a dipolar nonlinear lattice is studied and the regions of instability
are established. The existence and stability of bulk discrete solitons are
analyzed analytically and confirmed by numerical simulations. In a marked
contrast with the usual DNLS behavior (no dipolar interactions), we found a
region where the two fundamental modes are simultaneously unstable allowing
enhanced mobility across the lattice for large norm values. To study the
existence and properties of surface discrete solitons, an analysis of the dimer
configuration is performed. The properties of symmetric and antisymmetric modes
including the stability diagrams and bifurcations are investigated in closed
form. For the case of a bulk medium, properties of fundamental on-site and
inter-site localized modes are analyzed. On-site and inter-site surface
localized modes are studied finding that they do not exist when nonlocal
interactions predominate with respect to local ones.
