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Rogue wave

About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.


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Journal ArticleDOI
TL;DR: In this article, an analytical representation for the rogue waves of the Fokas-Lenells (FL) equation is presented by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution.
Abstract: The Fokas–Lenells (FL) equation arises as a model equation which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order [in the leading asymptotic order the nonlinear Schrodinger (NLS) equation results]. Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. When certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.

101 citations

Journal ArticleDOI
TL;DR: In this paper, the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) is presented, which is one of the integrable extensions of the nonlinear Schrodinger equation (NLSE).

101 citations

Journal ArticleDOI
TL;DR: The time-reversal invariance of the NLS is used to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space.
Abstract: The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrodinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

101 citations

Journal ArticleDOI
TL;DR: The results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrödinger equation with a modified nonlinearity parameter.
Abstract: We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of the two-component nonlinear Schrodinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route, we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS, and RW solutions. We then consider the RW solution as the starting point and derive AB, MS, and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrodinger equation with a modified nonlinearity parameter. Through this two-way approach we establish a broader understanding of these rational solutions, which will be of interest in a variety of situations.

101 citations

Journal ArticleDOI
TL;DR: In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics.

101 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023234
2022479
2021291
2020280
2019272
2018205