English
Related papers

Related papers: General high-order rogue waves and their dynamics …

200 papers

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique.…

Exactly Solvable and Integrable Systems · Physics 2016-11-03 K. Manikandan , M. Senthilvelan , R. A. Kraenkel

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

In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear…

Exactly Solvable and Integrable Systems · Physics 2012-02-07 Shuwei Xu , Jingsong He , Lihong Wang

Spatially-bounded rogue waves, i.e., rogue waves that arise in a limited region of a multi-dimensional space, are interesting and important from both theoretical and applied points of view. In this paper, we determine spatially-bounded…

Exactly Solvable and Integrable Systems · Physics 2025-11-24 Bo Yang , Jianke Yang

In this work, we construct various interesting localized wave structures of the Benjamin-Ono equation describing the dynamics of deep water waves. Particularly, we extract the rogue waves and generalized breather solutions with the aid of…

Exactly Solvable and Integrable Systems · Physics 2020-11-03 Sudhir Singh , K. Sakkaravarthi , K. Murugesan , R. Sakthivel

The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…

Exactly Solvable and Integrable Systems · Physics 2020-11-20 Juncai Pu , Jun Li , Yong Chen

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

The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…

Fluid Dynamics · Physics 2015-11-03 Y. Charles Li

By employing a mapping to classical anharmonic oscillators, we explore a class of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1 dimensions and, by extension, asymptotically in general dimensions. We discuss a possible way…

Mathematical Physics · Physics 2011-05-11 Patrick Johnson , Daniel Cole , Zohar Nussinov

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

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…

Fluid Dynamics · Physics 2017-03-17 Victor Shrira , Alexey Slunyaev

General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators,…

Exactly Solvable and Integrable Systems · Physics 2017-09-13 Jiguang Rao , Kuppuswamy Porsezian , Jingsong He

In this work, we numerically consider the initial value problem for nonlinear Schr\"odinger (NLS) type models arising in the physics of ultracold boson gases, with generic Gaussian wavepacket initial data. The corresponding Gaussian's width…

Pattern Formation and Solitons · Physics 2016-09-08 E. G. Charalampidis , J. Cuevas-Maraver , D. J. Frantzeskakis , P. G. Kevrekidis

The possibility of finite-time, dispersive blow up for nonlinear equations of Schroedinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the…

Analysis of PDEs · Mathematics 2014-01-20 Jerry L. Bona , Jean-Claude Saut , Gustavo Ponce , Christof Sparber

We study the existence and properties of rogue wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider Fokas-Lenells equation, the defocusing vector nolinear…

Exactly Solvable and Integrable Systems · Physics 2015-06-23 Fabio Baronio , Shihua Chen , Philippe Grelu , Stefan Wabnitz , Matteo Conforti

We study the cubic weakly nonlinear Schr\"odinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier space, we establish a {\em Large Deviations Principle} for…

Probability · Mathematics 2026-04-21 Fei Xu , Yong Li

In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants…

Exactly Solvable and Integrable Systems · Physics 2022-08-09 Junchao Chen , Bo Yang , Bao-Feng Feng

In the present paper, we attempt to construct both the general rogue wave solutions to the fully discrete nonlinear Schr\"odinger (fd-NLS) equation via the KP-Toda reduction method. First, we deduce the general breather solution of the…

Exactly Solvable and Integrable Systems · Physics 2022-07-20 Yasuhiro Ohta , Bao-Feng Feng

We show that the same special solution of the focusing nonlinear Schr\"{o}dinger equation that has been shown to arise in a certain near-field/large-order limit from soliton and Peregrine-like rogue wave solutions actually arises…

Exactly Solvable and Integrable Systems · Physics 2022-05-04 Deniz Bilman , Peter D. Miller

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