Akhmediev breathers and pulsed modulation instability

Here, we revisit and extend the breather formalism in an optical fiber context. Specifically, we have studied the applicability of the AB theory in describing MI in the pulsed regime by numerically studying the propagation dynamics of a weakly modulated hyperbolic secant pulse. It is clear from the evolution of the intensity distribution, that the weak initial modulation undergoes exponential growth and subsequent decay along the pulse envelope similar to that of an AB.