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.

Modulational instability and dynamics of multi-rogue wave solutions for the discrete Ablowitz-Ladik equation

Abstract: The higher order discrete rogue waves (RWs) of the integrable discrete Ablowitz-Ladik equation are reported using a novel discrete version of generalized perturbation Darboux transformation. The dynamical behaviors of strong and weak interactions of these RWs are analytically and numerically discussed, which exhibit the abundant wave structures. We numerically show that a small noise has the weaker effect on strong-interaction RWs than weak-interaction RWs, whose main reason may be related to main energy distributions of RWs. The interaction of two first-order RWs is shown to be non-elastic. Moreover, we find that the maximal number (Smax) of the possibly split first-order ones of higher order RWs is related to the number (Pmax) of peak points of their strongest-interaction cases, that is, Smax = (Pmax + 1)/2. The results will excite to further understand the discrete RW phenomena in nonlinear optics and relevant fields.

Dynamical criteria for rogue waves in nonlinear Schrödinger models

Abstract: We investigate rogue waves in deep water in the framework of the nonlinear Schrodinger (NLS) and Dysthe equations. Amongst the homoclinic orbits of unstable NLS Stokes waves, we seek good candidates to model actual rogue waves. In this paper we propose two selection criteria: stability under perturbations of initial data, and persistence under perturbations of the NLS model. We find that requiring stability selects homoclinic orbits of maximal dimension. Persistence under (a particular) perturbation selects a homoclinic orbit of maximal dimension all of whose spatial modes are coalesced. These results suggest that more realistic sea states, described by JONSWAP power spectra, may be analyzed in terms of proximity to NLS homoclinic data. In fact, using the NLS spectral theory, we find that rogue wave events in random oceanic sea states are well predicted by proximity to homoclinic data of the NLS equation.

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

Abstract: We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Prediction of Occurrences of Steep and High Waves in Deep Water

Abstract: Estimates for encounter probabilities of occurrence of steep and high waves in deep water for given sea states by using two different parametric models for the joint distribution of crest front steepness and wave height are presented. The parametric models are fitted to the same data set, with data from a zero‐downcross analysis of wave data obtained from measurements at sea on the Norwegian continental shelf. The probability of occurrence of waves with different crest front steepness are estimated with each parametric model for a family of JONSWAP spectra. An example is given where the probabilities of occurrence of “extreme waves,” which are considered to be critical to capsizing of smaller vessels, are estimated with one parametric model for sea states described by significant wave height and mean zero‐crossing period.