Hybrid two-component breather

The nonlinear coherent interaction of light with a dispersive and Kerr medium containing optical impurity atoms or semiconductor quantum dots has been considered. Using a generalized version of the perturbative reduction method, the nonlinear wave equation has been reduced to the coupled nonlinear Schrödinger equations. It has been shown that second-order derivatives play an essential role in describing the formation of the bound state of two breathers that oscillate with the sum and the difference of the frequencies and wave numbers. Resonant, nonresonant, and hybrid mechanisms for the formation of a two-component breather have been realized depending on the parameters of light and medium. Explicit analytical expressions for the profile and parameters of the nonlinear pulse have been given. The conditions for the formation of resonant, nonresonant, and hybrid nonlinear waves have been discussed. In particular case, the resonant vector breather coincides with the vector 0$\pi$-pulse of the self-induced transparency.