▎ 摘　　要

The different mechanisms that bring about the creation of optical nonlinear waves in a waveguide containing a graphene monolayer (or graphene-like two-dimensional material) are studied in the general case when resonant and nonresonant nonlinearities are simultaneously included. The conditions for the formation of optical hybrid, nonresonant, and resonant phase-modulated breathers in graphene, for waveguide transverse electric modes, are presented. It is shown that the characteristic parameters of these optical nonlinear waves depends on the graphene Kerr-type third-order susceptibility, the graphene conductivity, the reciprocal of Beer's absorption length, and the initial values of the ensemble of the atomic system and/or the semiconductor quantum dots that are embedded in the transition layer. In the case of the amplifier (active atomic system) transition layer, the conditions for the existence of a dark (topological) breather and the conditions when a nonlinear wave cannot be formed are determined. An explicit analytical expression for the profile of an optical nonlinear wave is also presented.