Related papers: Rogue waves and large deviations for 2D pure gravi…
Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects…
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schr\"odinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general…
In this paper we propose an extended Kundu-Eckhaus equation (KEE) for modeling the dynamics of skewed rogue waves emerging in the vicinity of a wave blocking point due to opposing current. The equation we propose is a KEE with an additional…
We predict the existence of linear discrete rogue waves governed by the discrete nonlinear Schrodinger equation. We discuss that Josephson effect is the underlying reason for the formation of such waves.
We present a simple representation for arbitrary-order rogue wave solution and study on the trajectories of them explicitly. We find that the global trajectories on temporal-spatial distribution all look like "X" shape for rogue waves.…
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…
The appearance of rogue waves is well known in oceanographics, optics, and cold matter systems. Here we show a possibility for the existence of atmospheric rogue waves.
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…
The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e.,…
We propose a new conceptual framework for the prediction of rogue waves and third-order space-time extremes of wind seas that relies on the Tayfun (1980) and Janssen (2009) models coupled with Adler-Taylor (2009) theory on the Euler…
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received intense attention in recent years in the context of…
The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…
Research on the statistics of extreme events using deterministic wave group methods has largely been simplified to vessels at zero or constant speed and heading. In contrast, free-running vessels move with six degrees-of-freedom (6-DoF),…
We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…
We present a numerical study of the evolution dynamics of ``optical rogue waves'', statistically-rare extreme red-shifted soliton pulses arising from supercontinuum generation in photonic crystal fiber [D. R. Solli et al. Nature Vol. 450,…
In this paper, we propose and apply a deep learning strategy for the early detection of the Draupner rogue (freak) wave, which is also known as the New Year's wave. We use a long short term memory (LSTM) network and show that Draupner rogue…
We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationaly unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped…
Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and…