Persistence of hydrodynamic envelope solitons: detection and rogue wave occurrence

关于下越和上越 rogue wave 的概率

On the probability of down-crossing and up-crossing rogue waves

本文通过深水方向波直接数值模拟，发现极端波在波浪后坡出现更深波谷的不对称性源于非线性组合谐波，会导致基于下越或上越零交叉方法的 rogue wave 概率估计存在显著差异。

Capturing rogue waves by multi-point statistics

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 rogue wave events in a statistically highly satisfactory manner. The key to the success of the approach is mapping the complexity of multi-point data onto the statistics of hierarchically ordered height increments for different time scales for which we can show that a stochastic cascade process with Markov properties is governed by a Fokker-Planck equation.…

Predicting rogue waves in random oceanic sea states

Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that is ``near'' NLS homoclinic data, while rogue waves do not occur for JONSWAP data that is ``far'' from NLS homoclinic data. We show the nonlinear spectral decomposition provides a simple criterium for predicting the occurrence and strength of rogu…

A Split-Step Fourier Scheme for the Dissipative Kundu-Eckhaus Equation and its Rogue Wave Dynamics

We investigate the rogue wave dynamics of the dissipative Kundu-Eckhaus equation. With this motivation, we propose a split-step Fourier scheme for its numerical solution. After testing the accuracy and stability of the scheme using an analytical solution as a benchmark problem, we analyze the chaotic wave fields generated by the modulation instability within the frame of the dissipative Kundu-Eckhaus equation. We discuss the effects of various parameters on rogue wave formation probability and we also discuss the role of dissipation on occurrences of such waves.

Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering

Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. As an exact breather solution of the one-dimensional focusing nonlinear Schrödinger equation with nonzero boundary conditions, the PS can be viewed as a soliton on finite background, i.e. a nonlinear superposition of a soliton and a monochromatic wave. A recent mathematical work showed that both nonzero boundary conditions and solitonic content are not pre-requisites for the PS occurrence. Instead, it has been d…

On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

We construct Darboux transformation of a coupled generalized nonlinear Schrödinger (CGNLS) equations and obtain exact analytic expressions of breather and rogue wave solutions. We also formulate the conditions for isolating these solutions. We show that the rogue wave solution can be found only when the four wave mixing parameter becomes real. We also investigate the modulation instability of the steady state solution of CGNLS system and demonstrate that it can occur only when the four wave mixing parameter becomes real. Our results give an evidence for the connection between the occurrence of…