Optical breathers and rogue waves via the modulation instability for a higher-order generalized nonlinear Schrodinger equation in an optical fiber transmission system

For describing the propagation of ultrashort pulses in a high-speed, long-distance optical fiber transmission system with the fourth-order dispersion, cubic-quintic nonlinearity, self-steepening and self-frequency shift, a higher-order generalized nonlinear Schrodinger equation is investigated. We get the rogue-wave solutions. Effects of the modulation instability on the optical rogue waves are studied: Increasing the growth rate of the modulation instability makes the existence time of the optical rogue wave shorter. We numerically derive the optical breathers in the chaotic wave fields via the modulation instability. Spectrum of the optical chaotic wave field can be used to indicate the appearance of the optical breather in the chaotic wave field. Optical rogue waves in the chaotic wave fields are also gotten via the modulation instability.