Composite rogue waves and modulation instability for the three-coupled Hirota system in an optical fiber

Abstract

We investigate the three-coupled Hirota system, which is applied to model the long distance communication and ultrafast signal routing systems governing the propagation of light pulses. With the aid of the Darboux dressing transformation, composite rogue wave solutions are derived. Spatial–temporal structures, including the four-petaled structure for the three-coupled Hirota system, are exhibited. We find that the four-petaled rogue waves occur in two of the three components, whereas the eye-shaped rogue wave occurs in the other one. The composite rogue waves can split up into two or three single rogue waves. The corresponding conditions for the occurrence of such phenomena are discussed and presented. We find that the relative position of every single rogue wave is influenced by the ratios of certain parameters. Besides, the linear instability analysis is performed, and our results agree with those from the baseband modulation instability theory.