Dark and bright excitons in systems with exchange and dipole-dipole interactions

Dark and bright soliton solutions (excitons) in one-dimensional chains of two-level atoms with exciton-exciton, dipole-dipole, and exchange interactions are obtained. It is shown that in some limiting cases evolution equations resulting from model Hamiltonians are reduced to the exactly integrable Ablowitz-Ladik model. Bloch oscillations of the excitons in inhomogeneous magnetic field and effects originated by the energy shift are discussed. An example of a multidimensional dark exciton is represented.