Few-cycle solitons in a dispersive medium with a permanent dipole moment

An integrable model of a two-level medium with a permanent dipole moment (PDM) is proposed. The model describes the evolution of electromagnetic field pulses beyond the slow envelope approximation. The dipole-dipole interaction is taken into account in the approximation of the nearest neighbors in the form of a quadratic dispersion. It is found that such a generalization of the reduced Maxwell-Bloch equations is completely integrable. Breather solutions are derived. These solutions are used to study the combined influence of the quadratic dispersion and PDM. It is found that the model possess a number of unique features, which give possibilities for controlling the shape of field pulses. In particular, it is found that the shape and amplitude of the field pulse depends on both the signs of the dipole-dipole interaction and the sign and value of the permanent dipole moment.