Rogue Waves for an Alternative System of Coupled Hirota Equations: Structural Robustness and Modulation Instabilities

Abstract

The Hirota system consists of two coupled, third‐order partial differential equations with cubic nonlinearities. Rogue wave (RW) modes for such coupled Hirota equations different from those usually considered in the literature are derived by the bilinear method. RWs exist in the defocusing regime (dispersion and nonlinearities of different signs), with an existence criterion closely related to the condition for baseband modulation instability (MI). This connection is examined further through numerical simulations. RW‐like structures can emerge from a plane wave background perturbed by random noise only if baseband MI is present. Furthermore, the development of an individual RW will not be “masked” by the growth of the noise if the MI itself is not too strong. Even more illuminating information is revealed with disturbance of a specified wavelength (or a narrow range of frequency input). A disturbance with wave numbers in the passband will not generate any coherent structures, but those in the baseband may generate an Akhmediev breather or a RW‐like structure.