Topic
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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TL;DR: The double-periodic solutions of the focusing nonlinear Schrödinger equation are constructed by using an algebraic method with two eigenvalues and the Lax spectrum is characterized and rogue waves arising on the background of such solutions are analyzed.
Abstract: The double-periodic solutions of the focusing nonlinear Schr\"odinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues. Furthermore, we characterize the Lax spectrum for the double-periodic solutions and analyze rogue waves arising on the background of such solutions. Magnification of the rogue waves is studied numerically.
77 citations
TL;DR: In this article, the formation of rogue waves in nonlinear hyperbolic systems with an application to nonlinear shallow-water waves is studied in the framework of nonlinear hypersphere.
Abstract: The formation of rogue waves is studied in the framework of nonlinear hyperbolic systems with an application to nonlinear shallow-water waves. It is shown that the nonlinearity in the random Riemann (travelling) wave, which manifests in the steeping of the face-front of the wave, does not lead to extreme wave formation. At the same time, the strongly nonlinear Riemann wave cannot be described by the Gaussian statistics for all components of the wave field. It is shown that rogue waves can appear in nonlinear hyperbolic systems only in the result of nonlinear wave–wave or/and wave–bottom interaction. Two special cases of wave interaction with a vertical wall (interaction of two Riemann waves propagating in opposite directions) and wave transformation in the basin of variable depth are studied in detail. Open problems of the rogue wave occurrence in nonlinear hyperbolic systems are discussed.
77 citations
TL;DR: In this article, a vector generalization of the Fokas-Lenells system, which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order, is investigated.
Abstract: In this paper, a vector generalization of the Fokas–Lenells system, which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order, is investigated. Higher-order soliton, breather, and rogue wave solutions of the coupled Fokas–Lenells system are derived via the n -fold Darboux transformation. Meanwhile the dynamic characteristics of those solitary wave solutions have been discussed.
77 citations
TL;DR: In this article, the authors considered the problem of giant wave formation on water of finite depth and suggested dispersive focusing in a nonlinear medium as a possible mechanism for giant wave generation.
77 citations
20 Jul 2018
TL;DR: In this article, the authors measured the statistics of these ultrafast rogue wave patterns with a time lens and developed a numerical model proving that the patterns of the ultra fast rogue waves were generated by the non-instantaneous relaxation of the saturable absorber together with the polarization mode dispersion of the cavity.
Abstract: Fiber lasers are convenient for studying extreme and rare events, such as rogue waves, thanks to the lasers’ fast dynamics. Indeed, several types of rogue wave patterns were observed in fiber lasers at different time-scales: single peak, twin peak, and triple peak. We measured the statistics of these ultrafast rogue wave patterns with a time lens and developed a numerical model proving that the patterns of the ultrafast rogue waves were generated by the non-instantaneous relaxation of the saturable absorber together with the polarization mode dispersion of the cavity. Our results indicate that the dynamics of the saturable absorber is directly related to the dynamics of ultrafast extreme events in lasers.
77 citations