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.

Weakly two-dimensional interaction of solitons in shallow water☆

Abstract: Nonlinear interactions of long-crested solitonic waves travelling in different directions in shallow water may serve as a possible mechanism of freak waves in certain sea areas. Several features of such interactions of equal amplitude Korteweg–de Vries (KdV) solitons in the framework of the Kadomtsev–Petviashvili equation are reviewed. In certain cases, nonlinear coupling produces a particularly high and steep wave hump. Interactions of equal amplitude solitons may lead to water surface elevations up to four times as high as the amplitude of the counterparts and the slope of the wave front may encounter eightfold increase. Exact expressions for the maximum slope in the case of interactions of unequal amplitude solitons are derived. The slope amplification for a certain class of interactions in the limiting case is twice as intense as the amplitude amplification. In the limiting case of exact resonance the interaction pattern is a new KdV soliton as in the case of the Mach stem. This feature allows to directly establish the extreme properties of the humps excited by nonlinear coupling. Evidence of such interactions and their possible consequences in realistic conditions are discussed.

Watch-hand-like optical rogue waves in three-wave interactions.

Abstract: We investigate the resonant interaction of three optical pulses of different group velocity in quadratic media and report on the novel watch-hand-like super rogue wave patterns In addition to having a giant wall-like hump, each rogue-wave hand involves a peak amplitude more than five times its background height We attribute such peculiar structures to the nonlinear superposition of six Peregrine-type solitons The robustness has been confirmed by numerical simulations This stability along with the non-overlapping distribution property may facilitate the experimental diagnostics and observation of these super rogue waves

Waves in hyperbolic and double negative metamaterials including rogues and solitons

Abstract: The topics here deal with some current progress in electromagnetic wave propagation in a family of substances known as metamaterials. To begin with, it is discussed how a pulse can develop a leading edge that steepens and it is emphasised that such self-steepening is an important inclusion within a metamaterial environment together with Raman scattering and third-order dispersion whenever very short pulses are being investigated. It is emphasised that the self-steepening parameter is highly metamaterial-driven compared to Raman scattering, which is associated with a coefficient of the same form whether a normal positive phase, or a metamaterial waveguide is the vehicle for any soliton propagation. It is also shown that the influence of magnetooptics provides a beautiful and important control mechanism for metamaterial devices and that, in the future, this feature will have a significant impact upon the design of data control systems for optical computing. A major objective is fulfiled by the investigations of the fascinating properties of hyperbolic media that exhibit asymmetry of supported modes due to the tilt of optical axes. This is a topic that really merits elaboration because structural and optical asymmetry in optical components that end up manipulating electromagnetic waves is now the foundation of how to operate some of the most successful devices in photonics and electronics. It is pointed out, in this context, that graphene is one of the most famous plasmonic media with very low losses. It is a two-dimensional material that makes the implementation of an effective-medium approximation more feasible. Nonlinear non-stationary diffraction in active planar anisotropic hyperbolic metamaterials is discussed in detail and two approaches are compared. One of them is based on the averaging over a unit cell, while the other one does not include sort of averaging. The formation and propagation of optical spatial solitons in hyperbolic metamaterials is also considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation ('effective medium') approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.

Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative

Abstract: In this letter, the designable integrability (DI) of the variable coefficient derivative nonlinear Schrodinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear Schrodinger equation (DNLSE). One novel feature of VCDNLSE with DI is that its coefficients can be designed artificially and analytically by using transformation. What is more, from the rogue wave and rational traveling solution of the DNLSE, we get two kinds of rogue waves of the VCDNLSE by this transformation. One kind of rogue wave has vanishing boundary condition, and the other non-vanishing boundary condition. The DI of the VCDNLSE also provides a possible way to control the profile of the rogue wave in physical experiments.