Abstract
The system of “integrable” coupled nonlinear Schrödinger 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 Schrödinger 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.
Highlights
Rogue waves or freak waves are extreme events in the ocean which are characterized by the emergence of large waves from an otherwise tranquil background [1,2,3]
Rogue waves originate from the context of water waves [1,2,3,6,7,8,9], these studies have been extended to other physical contexts like optical fibers [10,11,12]
It was known that a multi-component Manakov system can effectively model wave propagation in a multicore optical fiber [22]
Summary
Rogue waves or freak waves are extreme events in the ocean which are characterized by the emergence of large waves from an otherwise tranquil background [1,2,3]. In contrast to the single component case, rogue wave modes had been discovered for the coupled NLS equations in the defocusing regime [28,29,30,31] with group velocity mismatch between the two components This scenario is closely related to new ranges of modulation instability in the defocusing regime. Wavelength-division-multiplexed systems have been extended in the laboratory setting beyond the soliton formation regime, or more precisely to baseband and passband regimes for polarization modulation instabilities and the existence of rogue wave modes of the Manakov equations [32] In another multi-component investigation, optical dark rogue waves are demonstrated by a suitable injection of two colliding and modulated pump beams with orthogonal states of polarization [33].
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