We study the generation and propagation of hyperbolic secant solitons, Peregrine solitons, and various breathers in a coherently prepared three-level atomic system, where two lower states are coherently prepared prior to the injection of a strong pump field and a weak probe field. We show that a flat dispersion without gain and loss along with a large Kerr nonlinearity can be achieved in a broad range of probe field frequency. Moreover, optical hyperbolic secant solitons can be easily achieved in such a broad range at a very low light intensity and propagate stably. Due to the enhanced Kerr nonlinearity, we also show that it is possible to generate optical rogue waves and breathers with very weak light stimulus, which is three orders of magnitude smaller than that used in nonlinear fibers. Because the gain/absorption is negligible and the quantum noise of the probe field can be significantly suppressed, our work may pave the way for realizing solitons, rogue waves, and breathers at the quantum level.