  We study the role of the Dipolar-Induced Resonance (DIR) in a
quasi-one-dimensional system of ultracold bosons. We first describe the effect
of the DIR on two particles in a harmonic trap. Then, we consider a deep
optical lattice loaded with ultracold dipolar bosons. In order to describe this
system, we introduce a novel atom-dimer extended Bose-Hubbard model, which is
the minimal model correctly accounting for the DIR. We analyze the impact of
the DIR on the phase diagram at T=0 by exact diagonalization of a small-sized
system. We show that the DIR strongly affects this phase diagram. In
particular, we predict the mass density wave to occur in a narrow domain
corresponding to weak nearest-neighbor interactions, and the occurrence of a
collapse phase for stronger dipolar interactions.
