We first propose a two-dimensional spatial self-similar transformation of the Fokas system, which is translated into (1+1)-dimensional nonlinear Schrödinger equation, and construct its abundant line rogue waves excitation. It found that induced by Akhmediev breathers Kuznetsov-Ma solitons also have short life characteristics possessed for Peregrine other higher-order multi-rogue (1+1) dimension...

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during ex...

Observations of extreme, “freak” or “rogue waves” have typically depended on chance observations from ships at sea or from fixed oil or gas platforms. The observations have been so sparse that there are very few direct temporal or spatial measurements, and those that do exist are so infrequent that they have often been individually named: e.g. the “Draupner Wave.” Such named observations tend t...

Partial-rogue waves, i.e., waves that ``come from nowhere but leave with a trace", are analytically predicted and numerically confirmed in the Sasa-Satsuma equation. We show that, among class of rational solutions this equation can be expressed through determinants 3-reduced Schur polynomials, partial-rogue would arise if these certain orders, where associated generalized Okamoto polynomials ha...

The mathematical tools of large deviation theory for rare events are illustrated with some simple examples. These include discrete and continuous Gaussian processes, importance sampling, and evolution equations of the Langevin type. Some of these methods have been used in the study of rogue surface waves but it seems that large deviation theory could have much wider application in geophysical p...

We investigate the outbreak of anomalous quantum wave-function amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by competition between localization and mobility. The effective correlation length disorder ultimately responsible for bringing local strength to minimum, fueling occurrence extreme events much high...

We investigate the statistics of rogue waves occurring in inverse cascade surface gravity wave turbulence. In such statistically homogeneous, stationary and isotropic fields, low-frequency are generated by nonlinear interactions rather than directly forced a maker. This provides laboratory realization arguably simplest sea state, which long-time acquisitions performed compared with theoretical ...