Transition, coexistence, and interaction of vector localized waves arising from higher-order effects

Liu, Chong; Yang, Zhan-Ying; Zhao, Li-Chen; Yang, Wen-Li

doi:10.1016/j.aop.2015.06.008

Cited by 54 publications

(27 citation statements)

References 41 publications

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“…Additionally, recent hydrodynamical experiments and theoretical research confirm that the "super rogue waves" could be simulated by higher-order rational solutions [15][16][17][18][19][20][21][22][23][24][25][26][27]. More recently, with resort to the modulation instability (MI) analysis, state transition between brether/rogue wave and W-shaped soliton in high-order system, and state transition among different types of rogue-wave patterns in coupled system have been strictly demonstrated [28][29][30].…”

Section: Accepted Manuscriptmentioning

confidence: 92%

W-shaped soliton complexes and rogue-wave pattern transitions for the AB system

Wang

Liu

2017

Superlattices and Microstructures

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Section: Accepted Manuscriptmentioning

confidence: 92%

W-shaped soliton complexes and rogue-wave pattern transitions for the AB system

Wang

Liu

2017

Superlattices and Microstructures

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“…Liu et al have shown that the breathers can be converted into different types of nonlinear waves in the coupled NLS-MB system, including the multi-peak soliton, periodic wave, antidark soliton and W-shaped soliton [35]. In particular, they have indicated that the transition between the rogue waves and W-shaped solitons of the Hirota and coupled Hirota equations occurs as a result of the attenuation of MI growth rate to vanish in the zero-frequency perturbation region [36,37].…”

Section: Introductionmentioning

confidence: 96%

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

Wang

Zhang

et al. 2016

Nonlinear Dyn

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We study the AB system describing marginally unstable baroclinic wave packets in geophysical fluids and also ultrashort pulses in nonlinear optics. We show that the breather can be converted into different types of stationary nonlinear waves on constant backgrounds, including the multi-peak soliton, M-shaped soliton, W-shaped soliton and periodic wave. We also investigate the nonlinear interactions between these waves, which display some novel patterns due to the nonpropagating characteristics of the solitons: (1) Two antidark solitons can produce a W-shaped soliton instead of a higher-order antidark one; (2) the interaction between an antidark soliton and a W-shaped soliton can not only generate a higher-order antidark soliton, but also form a W-shaped soliton pair; and (3) the interactions between an oscillation W-shaped soliton and an oscillation M-shaped soliton show the multipeak structures. We find that the transition occurs at a modulational stability region in a low perturbation frequency region.

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“…Other than a combination of bright and dark RWs , a composite RW consisting of two fundamental RWs can also be formed for a focusing medium (

σ

′ > 0) . Vector RWs collide with dark‐bright solitons elastically and may be transformed to W‐shaped solitons . Although most works concentrate on the case with positive cubic nonlinearity, RWs for the defocusing regime (

σ

′ < 0) have also been derived in connection with modulation instability (MI) .…”

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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Transition, coexistence, and interaction of vector localized waves arising from higher-order effects

Cited by 54 publications

References 41 publications

W-shaped soliton complexes and rogue-wave pattern transitions for the AB system

W-shaped soliton complexes and rogue-wave pattern transitions for the AB system

Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

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

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