Related papers: A Predictable Rogue Wave and Generating Mechanisms
Rogue waves named by oceanographers are ubiquitous in nature and appear in a variety of different contexts such as water waves, liquid Helium, nonlinear optics, microwave cavities, etc. In this letter, we propose a novel type of exact…
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 extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the Rogue waves are localized surface waves, their theoretical models and experimental…
Rogue waves are solitary waves with extreme amplitudes, which appear to be a ubiquitous phenomenon in nonlinear wave propagation, with the requirement for a nonlinearity being their only unifying characteristics. While many mechanisms have…
A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume.…
Formation of giant waves in sea states with two spectral maxima, centered at close wave vectors ${\bf k}_0\pm\Delta {\bf k}/2$ in the Fourier plane, is numerically simulated using the fully nonlinear model for long-crested water waves [V.…
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 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…
Prediction is a central goal and a yet-unresolved challenge in the investigation of oceanic rogue waves. Here we define a horizon of predictability for oceanic rogue waves and derive, via extensive computational experiments, the first…
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…
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…
Freak waves, or rogue waves, are one of the fascinating manifestations of the strength of nature. These devastating walls of water appear from nowhere, are short-lived and extremely rare. Despite the large amount of research activities on…
The numerical simulation of the nonlinear dynamics of the sea surface has shown that the collision of two groups of relatively low waves with close but noncollinear wave vectors (two or three waves in each group with a steepness of about…
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…
The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schr\"odinger (MNLS) equation in one spatial-dimension with random initial conditions that are assumed to be normally distributed, with a spectrum…
A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence 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,…
We consider the problem of large wave prediction in two-dimensional water waves. Such waves form due to the synergistic effect of dispersive mixing of smaller wave groups and the action of localized nonlinear wave interactions that leads to…
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…
An analytical method for constructing various coherent localized solutions with short-lived characteristics is proposed based on a novel self-mapping transformation of the (2+1) dimensional KdV equation. The highlight of this method is that…