Related papers: Rogue waves emerging from the resonant interaction…

Rogue waves in (2+1)-dimensional three-wave resonant interactions are studied. General rogue waves arising from a constant background, from a lump-soliton background and from a dark-soliton background have been derived, and their dynamics…

Recent results of numerical simulations of fully nonlinear evolutionary equations for long-crested deep-water waves are discussed, where formation of extreme waves was observed. Several examples demonstrate that three-dimensionality of the…

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show…

In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…

Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here,…

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.

We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement…

Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue-like wave dynamics in a reaction-diffusion system…

In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for…

Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…

Ocean rogue waves are large and suddenly appearing surface gravity waves, which may cause severe damage to ships and other maritime structures. Despite years of research, the exact origin of rogue waves is still disputed. Linear…

Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…

General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a…

We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the…

As an example for complex systems with extreme events we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows grasping extreme…

General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then…

Optical rogue waves are rare yet extreme fluctuations in the value of an optical field. The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has…

Based on the bilinear operator and symbol calculation, some lump solutions are presented, rationally localized in all directions in the space, to a reduced (3+1)-dimensional KP equation. The lump solutions all contain six parameters, four…

Rogue waves are extreme ocean events characterized by the sudden formation of anomalously large crests, and remain an important subject of investigation in oceanography and mathematics. A central problem is to quantify the probability of…

We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…