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: In this paper, rogue wave solutions of the higher-order dispersive nonlinear Schrodinger equation are investigated, which describe the propagation of ultrashort optical pulse in optical fibers.
Abstract: In this paper, rogue wave solutions of the higher-order dispersive nonlinear Schrodinger equation are investigated, which describe the propagation of ultrashort optical pulse in optical fibers The Nth-order rogue wave solutions with 2N + 1 free complex parameters are constructed via the generalized Darboux transformation method As applications, rogue waves from the first to the fifth order are calculated according to different combinations of parameters In particular, rogue waves dynamics and several new spatial–temporal structures are also discussed and exhibited to make a comparison with those of the nonlinear Schrodinger equation
49 citations
TL;DR: The nonlinear TE of rogue waves in a cubic medium is reported, different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE.
Abstract: Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\"odinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a $\ensuremath{\pi}$-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
49 citations
TL;DR: In this paper, the long-term evolution of random wind waves is studied by direct numerical simulation within the framework of the Zakharov equation, where the emphasis is on kurtosis as a single characteristics of field departure from Gaussianity.
Abstract: [1] Long-term evolution of random wind waves is studied by direct numerical simulation within the framework of the Zakharov equation. The emphasis is on kurtosis as a single characteristics of field departure from Gaussianity. For generic wave fields generated by a steady or changing wind, kurtosis is found to be almost entirely due to bound harmonics. This observation enables one to predict the departure of evolving wave fields from Gaussianity, capitalizing on the already existing capability of wave spectra forecasting. Kurtosis rapidly adjusts to a sharp increase of wind and slowly decreases after a drop of wind. Typically kurtosis is in the range 0.1-0.3, which implies a tangible increase of freak wave probability compared to the Rayleigh distribution. Evolution of narrow-banded fields is qualitatively different from the generic case of wind waves: statistics is essentially non-Gaussian, which confirms that in this special case the standard kinetic equation paradigm is inapplicable.
48 citations
TL;DR: In this paper, the effects of the coefficients of the fourth-order dispersion, $$\gamma $$¯¯, and of the fifth-order nonlinear Schrodinger equation on the properties of Akhmediev breathers (ABs), Kuznetsov-Ma solitons and rogue-wave solutions were investigated.
Abstract: One-dimensional anisotropic Heisenberg ferromagnetic spin chain can be described by the fifth-order nonlinear Schrodinger equation, which is investigated in this paper. Through the Darboux transformation, we obtain the Akhmediev breathers (ABs), Kuznetsov–Ma (KM) solitons and rogue-wave solutions. Effects of the coefficients of the fourth-order dispersion, $$\gamma $$
, and of the fifth-order dispersion, $$\delta $$
, on the properties of ABs, KM solitons and rogue waves are discussed: (1) With $$\gamma $$
increasing, the AB exhibits stronger localization in time; (2) The propagation directions of an AB and a KM soliton change with the presence of $$\delta $$
; and (3) Enhancement of $$\gamma $$
makes the existence time of the rogue waves shorter, while enhancement of $$\delta $$
increases the existence time of the rogue waves.
48 citations
TL;DR: In this article, a (2 + 1)-dimensional reduced YTSF equation is studied and the lump solutions more general than those in the existing literature, which orient in all directions of space and time with more parameters.
Abstract: Lattices and liquids are common in physics, engineering, science, nature and life. The Yu-Toda-Sasa-Fukuyama (YTSF) equation describes the elastic quasiplane wave in a lattice or interfacial wave in a two-layer liquid. A (2 + 1)-dimensional reduced YTSF equation is studied in this paper. With symbolic computation, we get the lump solutions more general than those in the existing literature, which orient in all directions of space and time with more parameters. Via the lump solutions, we get the moving path of lump waves, lumpoff solutions and moving path of the lumpoff waves, which describe interactions between one stripe soliton and a lump wave. When the lump solutions produce the one stripe solitons, the lumpoff solutions are constructed. When a pair of stripe solitons cut lump wave, the rogue wave emerges. Time and place for the rogue wave to appear can be obtained from the coordinates of the interaction points between a pair of stripe solitons and the lump wave.
48 citations