English
Related papers

Related papers: The optical rogue wave patterns in coupled defocus…

200 papers

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We…

Pattern Formation and Solitons · Physics 2018-09-19 E. G. Charalampidis , J. Lee , P. G. Kevrekidis , C. Chong

We study the standing periodic waves in the semi-discrete integrable system modelled by the Ablowitz-Ladik equation. We have related the stability spectrum to the Lax spectrum by separating the variables and by finding the characteristic…

Exactly Solvable and Integrable Systems · Physics 2023-03-31 Jinbing Chen , Dmitry E. Pelinovsky

We study numerically the dynamics of a one-electron wave packet in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schr\"{o}dinger equation is…

Disordered Systems and Neural Networks · Physics 2007-05-23 F. A. B. F. de Moura , M. L. Lyra , F. Dominguez-Adame , V. A. Malyshev

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity, $ U_0…

Fluid Dynamics · Physics 2011-10-27 Miguel Onorato , Davide Proment , Alessandro Toffoli

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…

Fluid Dynamics · Physics 2018-01-24 Giovanni Dematteis , Tobias Grafke , Eric Vanden-Eijnden

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…

Chaotic Dynamics · Physics 2015-05-13 A. Grönlund , B. Eliasson , M. Marklund

The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e.,…

Fluid Dynamics · Physics 2017-10-05 Alexey Slunyaev , Alexander Dosaev

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…

Fluid Dynamics · Physics 2007-08-01 V. P. Ruban

We show how a variety of stable spatio-temporal periodic patterns can be created in 2D-lattices of coupled oscillators with non-homogeneous coupling delays. A "hybrid dispersion relation" is introduced, which allows studying the stability…

Dynamical Systems · Mathematics 2017-10-31 Markus Kantner , Serhiy Yanchuk , Eckehard Schöll

The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In oceanography it is known as the Alber equation, and its…

Numerical Analysis · Mathematics 2026-03-31 Agissilaos Athanassoulis , Fotini Karakatsani , Irene Kyza

A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…

Pattern Formation and Solitons · Physics 2015-05-18 R. Marangell , C. K. R. T. Jones , H. Susanto

Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…

Pattern Formation and Solitons · Physics 2016-04-20 Mei Duanmu , Nathaniel Whitaker , Panos Kevrekidis , Anna Vainchtein , Jonathan Rubin

The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We consider the dynamics of weakly nonlinear wave packets, and…

Pattern Formation and Solitons · Physics 2009-11-11 S. D. Griffiths , R. H. J. Grimshaw , K. R. Khusnutdinova

We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of…

Chaotic Dynamics · Physics 2014-10-30 Stefano Lepri , Arkady Pikovsky

Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is…

Exactly Solvable and Integrable Systems · Physics 2025-08-05 Hans Werner Schuermann , Valery Serov

In this work, we analyze the asymptotic behaviors of high-order rogue wave solutions with multiple large parameters and discover novel rogue wave patterns, including claw-like, OTR-type, TTR-type, semi-modified TTR-type, and their modified…

Exactly Solvable and Integrable Systems · Physics 2024-05-31 Huian Lin , Liming Ling

We construct and discuss a semi-rational, multi-parametric vector solution of coupled nonlinear Schr\"odinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, and…

Exactly Solvable and Integrable Systems · Physics 2013-08-09 Fabio Baronio , Antonio Degasperis , Matteo Conforti , Stefan Wabnitz

Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schr\"odinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general…

Pattern Formation and Solitons · Physics 2016-11-23 Marco Bertola , Gennady El , Alexander Tovbis

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…

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…