Rogue waves for a long wave–short wave resonance model with multiple short waves

Chan, Hiu Ning; Ding, Edwin; Kedziora, David J.; Grimshaw, Roger; Chow, K. W.

doi:10.1007/s11071-016-2865-3

Cited by 29 publications

(25 citation statements)

References 29 publications

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“…Similar increment in amplitude due to coupling was also found in other coupled systems such as the long wave-short wave resonance model with two short wave components [41] and a system of coupled derivative nonlinear Schrödinger equations [38].…”

Section: Enhancement Of Amplitudesupporting

confidence: 76%

“…From Equation (3), if a + ib is a root of the dispersion relation, then a − ib will also be admissible and provides another rogue wave solution. This phenomenon was also observed in other multi-component system [38][39][40][41]. Such multi-rogue-wave scenarios are not allowed in the two-component Manakov system.…”

Section: Extension Of Existence Regimementioning

confidence: 54%

“…The connection was established theoretically in several dynamical systems [38,39,41,42]. This section focuses on the role of baseband modulation instability in the formation of rogue wave.…”

Section: Baseband Modulation Instabilitymentioning

confidence: 99%

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

Chan¹,

Chow²

2017

Applied Sciences

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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.

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Section: Enhancement Of Amplitudesupporting

confidence: 76%

Section: Extension Of Existence Regimementioning

confidence: 54%

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

Chan¹,

Chow²

2017

Applied Sciences

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“…Noise with long wavelength and small frequency will grow as a result of interplay between dispersive and nonlinear effects. This phenomenon also arises in many other evolution systems .…”

Section: Existence Regime and The Connection With Modulation Instabilitymentioning

confidence: 71%

“…Historically, it was actually known in the 1980s that coupling of nonlinear evolution equations might induce new regions of MIs [18]. As such instabilities have been demonstrated to be intimately connected with the occurrence of RWs for various systems, e.g., NLSE [19], coupled NLSEs [20], derivative NLSE [21], long wave-short wave resonance model [22,23], coupled derivative NLSEs [24], it is valuable to document these effects for the present version of coupled Hirota equations too (Eq. 2).…”

Section: Introductionmentioning

confidence: 99%

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

Chan

Chow

2017

Stud Appl Math

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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.

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Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system

et al. 2018

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Rogue waves for a long wave–short wave resonance model with multiple short waves

Cited by 29 publications

References 29 publications

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

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

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

Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system

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