Related papers: Rogue waves in the Davey-Stewartson equation
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been…
We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold Darboux transformation formula. We consider two types of double periodic solutions as seed solutions. We identify the squared…
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…
Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to the aperiodic distributions of prime elements in complex quadratic fields. Specifically, by studying light diffraction from…
We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing, may…
We consider instability and localized patterns arising from long wave-short wave (LWSW) resonance in the non-integrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to…
We report new rogue wave patterns in the nonlinear Schr\"{o}dinger equation. These patterns include heart-shaped structures, fan-shaped sectors, and many others, that are formed by individual Peregrine waves. They appear when multiple…
The Gerdjikov-Ivanov (GI) system of $q$ and $r$ is defined by a quadratic polynomial spectral problem with $2 \times 2$ matrix coefficients. Each element of the matrix of n-fold Darboux transformation of this system is expressed by a ratio…
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…
Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these…
In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schr\"odinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the…
We consider a two-level atomic system, interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field, admits an envelope profile…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are…
A rogue wave formation mechanism is proposed within the framework of a coupled nonlinear Schrodinger (CNLS) system corresponding to the interaction of two waves propagating in oblique directions in deep water. A rogue condition is…
The evolution of crossing sea states and the emergence of rogue waves in such systems are studied via numerical simulations performed using a higher order spectral method to solve the free surface Euler equations with a flat bottom. Two…
We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on…
In this paper we propose an efficient tomographic approach for the early detection of 2D rogue waves. The method relies on the principle of detecting conical spectral features before rogue wave becomes evident in time. More specifically,…
We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…