  We exploit a few- to many-body approach to study strongly interacting dipolar
bosons in the quasi-one-dimensional system. The dipoles attract each other
while the short range interactions are repulsive. Solving numerically the
multi-atom Schr\"{o}dinger equation, we discover that such systems can exhibit
not only the well known bright soliton solutions but also novel quantum
droplets for a strongly coupled case. For larger systems, basing on microscopic
properties of the found few-body solution, we propose a new equation for a
density amplitude of atoms. It accounts for fermionization for strongly
repelling bosons by incorporating the Lieb-Liniger energy in a local density
approximation and approaches the standard Gross-Pitaevskii equation (GPE) in
the weakly interacting limit. Not only does such a framework provide an
alternative mechanism of the droplet stability, but it also introduces means to
further analyze this previously unexplored quantum phase. In the limiting
strong repulsion case, yet another simple multi-atom model is proposed. We
stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in
this case.
