Ultraslow kuznetsov-ma solitons and ahkmediev breathers in a cold three-state medium exposed to nanosecond optical pulses

We investigate the formation of the Kuznetsov-Ma solitons and Ahkmediev breathers in a cold ?-type three-level atomic system that interacts with a probe field of nanosecond pulse duration and a strong continuous-wave driving field via an electromagnetically induced transparency process. Within the framework of the Hirota equation, exact explicit analytical solutions of these breathers are obtained, showing different amplitude and oscillatory characteristics. Numerical simulations confirm the stability of both types of breathers against non-integrable perturbations that are caused by the nonvanishing decay rates of atomic states. We show that both breathers thus generated can propagate at a quite low group velocity.