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 article, a conceptually new approach to the formation of rogue waves (RWs) is proposed, in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical inverse scattering transform (IST) procedure relying on a spatial periodization of the object under consideration.
Abstract: The nonlinear Schrodinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.
82 citations
TL;DR: Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrödinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.
Abstract: Rogue waves are observed as light propagates in the extreme nonlinear regime that occurs when a photorefractive ferroelectric crystal is undergoing a structural phase transition. The transmitted spatial light distribution contains bright localized spots of anomalously large intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The isolated wave events form as out-of-equilibrium response and disorder enhance the Kerr-saturated nonlinearity at the critical point. Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrodinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.
82 citations
TL;DR: In this paper, an analytical representation for the rogue waves of the Fokas-Lenells (FL) equation is presented, which is constructed 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 eqution 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 Schr\"odinger (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.
82 citations
TL;DR: In this paper, a statistical analysis of some of the largest waves occurring during 793h of surface elevation measurements collected during 14 severe storms in the North Sea is presented, where the distribution of extreme waves are modelled by fitting generalized pareto distributions, and extreme value distributions and return periods are given for freak waves in terms of empirical fitted parameters.
82 citations
TL;DR: In an array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue wave by determining the required input profile of the electric field.
Abstract: In an array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue wave Input field almost homogeneously distributed over hundreds of waveguides concentrates practically all the energy into a single waveguide at the output plane of the structure We determine the required input profile of the electric field to achieve this We illustrate the phenomenon by modeling the array by direct numerical simulations of the discrete nonlinear Schrodinger equation
82 citations