Modulation instability and breathers synchronization of the nonlinear Schrödinger Maxwell-Bloch equation

Nonlinear Schrödinger Maxwell-Bloch equation with a perturbation has been discussed in this paper. By virtue of the Darboux transformation and Joukowsky transformation, three kinds of N-order breathers have been attained. Propagation and interaction of the breathers have been obtained: spectrum parameter determined the types of the breathers; spectrum parameter has affect on the breathers synchronization/asynchronization; breather asynchronization is consistent with theories for relations of modulation instability and rogue waves; Modulation instability has also been discussed.