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Related papers: Rogue Waves In Nonlinear Schr\"odinger Models with…

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General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…

Exactly Solvable and Integrable Systems · Physics 2014-04-14 Gui Mu , Zhenyun Qin , Roger Grimshaw

Rogue wave patterns in the nonlinear Schr\"{o}dinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is…

Exactly Solvable and Integrable Systems · Physics 2021-01-06 Bo Yang , Jianke Yang

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5…

Fluid Dynamics · Physics 2017-03-30 A. Slunyaev , E. Pelinovsky , A. Sergeeva , A. Chabchoub , N. Hoffmann , M. Onorato , N. Akhmediev

Gross-Pitaevskii equation for Bose-Einstein condensate confined in elongated cigar-shaped trap is reduced to an effective system of nonlinear equations depending on only one space coordinate along the trap axis. The radial distribution of…

Soft Condensed Matter · Physics 2007-05-23 A. M. Kamchatnov , V. S. Shchesnovich

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

We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the…

Quantum Gases · Physics 2022-03-23 Vishwanath Shukla , Sergey Nazarenko

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

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

We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…

Pattern Formation and Solitons · Physics 2022-12-16 Yan-Hong Qin , Liming Ling , Li-Chen Zhao

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

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled…

Pattern Formation and Solitons · Physics 2016-04-06 K. Manikandan , P. Muruganandam , M. Senthilvelan , M. Lakshmanan

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

This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue…

Exactly Solvable and Integrable Systems · Physics 2019-03-18 Bo Yang , Jianke Yang

We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavior of a spectrum evolving from a broad class of initial data,…

Fluid Dynamics · Physics 2021-07-07 B. V. Semisalov , V. N. Grebenev , S. B. Medvedev , S. V. Nazarenko

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

We explore the existence and dynamical generation of rogue waves (RWs) within a one dimensional quantum droplet bearing environment. RWs are computed by deploying a spacetime fixed point scheme to the relevant extended Gross Pitaevskii…

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 Zhenya Yan , V. V. Konotop , N. Akhmediev

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 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 construct spatiotemporal localized envelope solutions of a (3+1)-dimensional nonlinear Schr\"{o}dinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique.…

Exactly Solvable and Integrable Systems · Physics 2016-08-24 K. Manikandan , M. Senthilvelan