Rogue Wave Modes for the Coupled Nonlinear Schrodinger System with Three Components: A Computational Study

The system of integrable coupled nonlinear Schrodinger equations (Manakov system) with three components in the defocusing regime is considered. Rogue wave solutions exist for a restricted range of group velocity mismatch, and the existence condition correlates precisely with the onset of baseband modulation instability. This assertion is further elucidated numerically by evidence based on the generation of rogue waves by a single mode disturbance with a small frequency. This same computational approach can be adopted to study coupled nonlinear Schrodinger equations for the non-integrable regime, where the coefficients of self-phase modulation and cross-phase modulation are different from each other. Starting with a wavy disturbance of a finite frequency corresponding to the large modulation instability growth rate, a breather can be generated. The breather can be symmetric or asymmetric depending on the magnitude of the growth rate. Under the presence of a third mode, rogue wave can exist under a larger group velocity mismatch between the components as compared to the two-component system. Furthermore, the nonlinear coupling can enhance the maximum amplitude of the rogue wave modes and bright four-petal configuration can be observed.