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Appl. Sci. 2017, 7(6), 559; doi:10.3390/app7060559

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

Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong, China
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Received: 13 April 2017 / Revised: 9 May 2017 / Accepted: 16 May 2017 / Published: 29 May 2017
(This article belongs to the Special Issue Guided-Wave Optics)
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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. View Full-Text
Keywords: rogue waves; manakov system; modulation instability; numerical simulation rogue waves; manakov system; modulation instability; numerical simulation
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Chan, H.N.; Chow, K.W. Rogue Wave Modes for the Coupled Nonlinear Schrödinger System with Three Components: A Computational Study. Appl. Sci. 2017, 7, 559.

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