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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

General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of…

Exactly Solvable and Integrable Systems · Physics 2018-08-29 Junchao Chen , Yong Chen , Bao-Feng Feng , Ken-ichi Maruno , Yasuhiro Ohta

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 work, we study the dynamics of rogue waves in the partially $\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux transformation method, general rogue waves in the partially $\cal{PT}$-symmetric nonlocal DS…

Mathematical Physics · Physics 2017-10-20 Bo Yang , Yong Chen

In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…

Pattern Formation and Solitons · Physics 2022-03-09 Chong Liu , Shao-Chun Chen , Xiankun Yao , Nail Akhmediev

In this paper, by considering the potential application in two mode nonlinear waves in nonlinear fibers under a certain case, we define a coupled nonlinear Schr\"odinger equation(called Frobenius NLS equation) including its Lax pair.…

Exactly Solvable and Integrable Systems · Physics 2017-10-31 Huijuan Zhou , Chuanzhong Li

We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen-Lee-Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks…

Exactly Solvable and Integrable Systems · Physics 2021-11-10 Weiqi Peng , Juncai Pu , Yong Chen

This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions of the coupled nonlinear Schr\"odinger (CNLS) equation in the presence of multiple large internal parameters. We report several new high-order RW…

Exactly Solvable and Integrable Systems · Physics 2026-04-30 Zixuan Deng , Huian Lin , Liming Ling

Based on the bilinear operator and symbol calculation, some lump solutions are presented, rationally localized in all directions in the space, to a reduced (3+1)-dimensional KP equation. The lump solutions all contain six parameters, four…

Exactly Solvable and Integrable Systems · Physics 2017-05-24 Xiaoen Zhang , Yong Chen , Xiaoyan Tang

This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions for any multi-component nonlinear Schr\"odinger equation (denoted as $n$-NLSE) with multiple internal large parameters and reports some new RW…

Exactly Solvable and Integrable Systems · Physics 2025-02-19 Huian Lin , Liming Ling

We report rogue-wave and lump patterns associated with Umemura polynomials, which arise in rational solutions of the third Painlev\'{e} equation. We first show that in many integrable equations such as the nonlinear Schr\"odinger equation…

Exactly Solvable and Integrable Systems · Physics 2026-04-28 Bo yang , Jianke Yang

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

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrodinger (MNLS) equation in terms of fractional forms of determinants.…

Exactly Solvable and Integrable Systems · Physics 2017-04-19 Xiao-Yong Wen , Yunqing Yang , Zhenya Yan

In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schr\"odinger equation with several higher-order nonlinear effects representing…

Exactly Solvable and Integrable Systems · Physics 2013-06-06 L. H. Wang , K. Porsezian , J. S. 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

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

An analytical method for constructing various coherent localized solutions with short-lived characteristics is proposed based on a novel self-mapping transformation of the (2+1) dimensional KdV equation. The highlight of this method is that…

Pattern Formation and Solitons · Physics 2024-05-22 Jie-Fang Zhang , Mei-zhen Jin , Meng-yang Zhang

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

The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…

Exactly Solvable and Integrable Systems · Physics 2019-12-04 Junchao Chen , Liangyuan Chen , Bao-Feng Feng , Ken-ichi Maruno

We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and…

Pattern Formation and Solitons · Physics 2017-03-31 Yunqing Yang , Zhenya Yan , Boris A. Malomed