English
Related papers

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

200 papers

We report the experimental observation of vector extensions of Peregrine solitons in highly particle-imbalanced, pairwise immiscible three-component repulsive Bose-Einstein condensates (BECs). The possibility of an effectively attractive…

Quantum Gases · Physics 2025-10-30 G. A. Bougas , G. C. Katsimiga , S. Mossman , P. Engels , P. G. Kevrekidis , S. I. Mistakidis

We find that diverse nonlinear waves, such as soliton, Akhmediev breather, and rogue waves (RWs), can emerge and interplay with each other in a two-mode coupled system. It provides a good platform to study interaction between different…

Pattern Formation and Solitons · Physics 2015-06-23 Li-Chen Zhao , Jie Liu

We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue…

Optics · Physics 2015-06-24 S. Efe , C. Yuce

The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…

Exactly Solvable and Integrable Systems · Physics 2015-06-17 Zhenya Yan , Chaoqing Dai

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system.…

Exactly Solvable and Integrable Systems · Physics 2017-03-31 Xiao-Yong Wen , Zhenya Yan , Boris A. Malomed

This paper is dedicated to study higher-order rogue wave solutions of the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and stimulated Raman scattering terms. By using the generalized…

Exactly Solvable and Integrable Systems · Physics 2014-09-18 Xin Wang , Yong Chen

General high-order rogue waves of the NLS-Boussinesq equation are obtained by the KP-hierarchy reduction theory. These rogue waves are expressed with the determinants, whose entries are all algebraic forms. It is found that the fundamental…

Exactly Solvable and Integrable Systems · Physics 2017-10-25 Xiaoen Zhang , Yong Chen

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…

Exactly Solvable and Integrable Systems · Physics 2023-09-06 Bo Yang , Jianke Yang

The height of an $n$th-order fundamental rogue wave $q_{\rm rw}^{[n]}$ for the nonlinear Schr\"odinger equation, namely $(2n+1)c$, is proved directly by a series of row operations on matrices appeared in the $n$-fold Darboux transformation.…

Exactly Solvable and Integrable Systems · Physics 2017-04-20 Lihong Wang , Chenghao Yang , Ji Wang , Jingsong He

In this work, we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schr\"odinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as…

Pattern Formation and Solitons · Physics 2014-10-23 R. B. Mareeswaran , E. G. Charalampidis , T. Kanna , P. G. Kevrekidis , D. J. Frantzeskakis

In this paper, we propose the existence and discuss the properties of rogue quantum gravitational waves. More specifically, we numerically solve the Schr\"odinger-Newton system of equations using a spectral scheme with a $4^{th}$ order…

General Physics · Physics 2023-01-25 Cihan Bayindir , Fatih Ozaydin , Azmi Ali Altintas , Metin Arik

The collision dynamics of two first-order rogue waves (RWs) with opposite incident momentum in two-component Bose-Einstein condensates (BECs) is studied by solving the two-component one-dimensional Gross-Pitaevskii (GP) equation. It is…

Quantum Gases · Physics 2025-06-11 Zhihao Zhang , Tiantian Li , Xiao-Dong Bai , Yunbo Zhang , Denglong Wang

A nonlinear Schr\"odinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can…

Fluid Dynamics · Physics 2017-04-14 V. P. Ruban

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

The double-periodic solutions of the focusing nonlinear Schrodinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues.…

Exactly Solvable and Integrable Systems · Physics 2019-12-04 Jinbing Chen , Dmitry E. Pelinovsky , Robert E. White

This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…

Analysis of PDEs · Mathematics 2024-08-13 Deniz Bilman , Peter D. Miller

We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability…

Optics · Physics 2016-02-12 Christopher J. Gibson , Alison M. Yao , Gian-Luca Oppo

We study fundamental rogue-wave solutions of the focusing nonlinear Schr\"odinger equation in the limit that the order of the rogue wave is large and the independent variables $(x,t)$ are proportional to the order (the far-field limit). We…

Exactly Solvable and Integrable Systems · Physics 2021-03-02 Deniz Bilman , Peter D. Miller

Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it…

Pattern Formation and Solitons · Physics 2021-09-14 Mark J. Ablowitz , Justin T. Cole

In this paper, novel rogue wave patterns in the nolocal nonlinear Schr\"odinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple…

Pattern Formation and Solitons · Physics 2025-03-14 Tingyou Wang , Zhenyun Qin , Gui Mu , Fuzhuang Zheng , Zhijun Qiao