English
Related papers

Related papers: High-order Rogue Waves in Vector Nonlinear Schr\"o…

200 papers

General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then…

Exactly Solvable and Integrable Systems · Physics 2015-06-05 Yasuhiro Ohta , Jianke Yang

General rogue waves in the Davey-Stewartson-II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the…

Exactly Solvable and Integrable Systems · Physics 2015-06-12 Yasuhiro Ohta , Jianke Yang

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

In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of…

Exactly Solvable and Integrable Systems · Physics 2013-04-10 Yongshuai Zhang , Lijuan Guo , Shuwei Xu , Zhiwei Wu , Jingsong HE

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…

Pattern Formation and Solitons · Physics 2015-06-22 Mark J. Ablowitz , Theodoros P. Horikis

Formation of giant waves in sea states with two spectral maxima, centered at close wave vectors ${\bf k}_0\pm\Delta {\bf k}/2$ in the Fourier plane, is numerically simulated using the fully nonlinear model for long-crested water waves [V.…

Fluid Dynamics · Physics 2015-05-13 V. P. Ruban

We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…

Exactly Solvable and Integrable Systems · Physics 2014-07-23 Fabio Baronio , Matteo Conforti , Antonio Degasperis , Sara Lombardo , Miguel Onorato , Stefan Wabnitz

Using the generalised nonlinear Schr\"odinger equation, we investigate how the effect of third-order dispersion, self-steepening, and Raman-induced-self-frequency shift have an impact on the higher-order rogue waves. We observe that…

Pattern Formation and Solitons · Physics 2022-10-04 Amdad Chowdury , Wonkeun Chang , Marco Battiato

Rogue wave patterns in the nonlinear Schr\"{o}dinger (NLS) equation and the derivative NLS equation are analytically studied. It is shown that when the free parameters in the analytical expressions of these rogue waves are large, these…

Pattern Formation and Solitons · Physics 2020-09-15 Bo Yang , Jianke Yang

We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schr\"odinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the…

Exactly Solvable and Integrable Systems · Physics 2015-06-22 Jingsong He , Lijuan Guo , Yongshuai Zhang , Amin Chabchoub

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…

Exactly Solvable and Integrable Systems · Physics 2022-07-28 N. Sinthuja , M. Senthilvelan

Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These…

Exactly Solvable and Integrable Systems · Physics 2018-11-14 Bo Yang , Jianke Yang

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 Zhenya Yan

We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…

Pattern Formation and Solitons · Physics 2014-07-15 Li-Chen Zhao , Chong Liu , Zhan-ying Yang

In this work, we study a prototypical, experimentally accessible scenario that enables the systematic generation of so-called high-order rogue waves in atomic Bose-Einstein condensates. These waveforms lead to significantly and controllably…

Pattern Formation and Solitons · Physics 2025-02-21 Jimmie Adriazola , Panayotis Kevrekidis

In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…

Pattern Formation and Solitons · Physics 2019-02-15 C. B. Ward , P. G. Kevrekidis

This paper delves into the study of multi-component derivative nonlinear Schrodinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation (DT) method, we derive higher-order vector rogue wave…

Exactly Solvable and Integrable Systems · Physics 2023-12-20 Lin Huian , Ling Liming

We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…

Exactly Solvable and Integrable Systems · Physics 2013-01-08 Nikolay K. Vitanov , Amin Chabchoub , Norbert Hoffmann

Rogue waves (RWs) can form on the ocean surface due to quasi-four wave resonant interaction or superposition principle. Both mechanisms have been acutely studied. The first of the two is known as the nonlinear focusing mechanism and leads…

Fluid Dynamics · Physics 2024-05-21 Yuchen He , Jinghua Wang , Jingsong He , Ye Li , Xingya Feng , Amin Chabchoub

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system…

Exactly Solvable and Integrable Systems · Physics 2015-10-23 Wei-Ping Zhong , Milivoj Belić , Boris A. Malomed