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Related papers: Rogue waves in a two-component Manakov system with…

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We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter…

Exactly Solvable and Integrable Systems · Physics 2016-07-15 K. Manikandan , M. Senthilvelan , R. A. Kraenkel

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

We have investigated the ($2+1$)-dimensional variable coefficient coupled nonlinear Schr\"{o}dinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient…

Pattern Formation and Solitons · Physics 2016-05-25 Kanchan Kumar De , Thokala Soloman Raju , C. N. Kumar , Prasanta K. Panigrahi

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

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 show that universal rogue wave patterns exist in integrable systems. These rogue patterns comprise fundamental rogue waves arranged in shapes such as triangle, pentagon and heptagon, with a possible lower-order rogue wave at the center.…

Exactly Solvable and Integrable Systems · Physics 2021-07-14 Bo Yang , Jianke Yang

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

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones…

Pattern Formation and Solitons · Physics 2015-01-26 Liming Ling , Boling Guo , Li-Chen Zhao

We show that new types of rogue wave patterns exist in integrable systems, and these rogue patterns are described by root structures of Okamoto polynomial hierarchies. These rogue patterns arise when the $\tau$ functions of rogue wave…

Exactly Solvable and Integrable Systems · Physics 2022-08-08 Bo Yang , Jianke Yang

In this brief report we study numerically the spontaneous emergence of rogue waves in (i) modulationally unstable plane wave at its long-time statistically stationary state and (ii) bound-state multi-soliton solutions representing the…

Pattern Formation and Solitons · Physics 2022-12-09 D. S. Agafontsev , A. A. Gelash

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

Based on modulation instability analysis and generalized Darboux transformation, we derive a hierarchy of rogue wave solutions for a variable-coefficients coupled Hirota equations. The explicit first-order rogue wave solution is presented,…

Exactly Solvable and Integrable Systems · Physics 2015-12-29 Xin Wang , Yong Chen

We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…

Pattern Formation and Solitons · Physics 2020-08-17 K. Sakkaravarthi , R. Babu Mareeswaran , T. Kanna

Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are…

Pattern Formation and Solitons · Physics 2018-04-04 Jinbing Chen , Dmitry E. Pelinovsky

The spectra of rogue waves of Manakov equations that exist in both focusing or defocusing regimes are derived in analytic form. These spectra are asymmetric during their whole expansion-contraction cycle. They have triangular shape at each…

Pattern Formation and Solitons · Physics 2023-11-09 Shao-Chun Chen , Chong Liu , Nail Akhmediev

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the…

Pattern Formation and Solitons · Physics 2016-05-31 Li-Chen Zhao , Boling Guo , Liming Ling

We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We…

Exactly Solvable and Integrable Systems · Physics 2014-12-04 K. Manikandan , P. Muruganandam , M. Senthilvelan , M. Lakshmanan

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

In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified…

Mathematical Physics · Physics 2013-12-24 Xin Wang , Yuqi Li , Yong Chen

The formation of coherent structures in noise driven phenomena and in Turbulence is a complex and fundamental question. A particulary important structure is the so-called Rogue Wave (RW) that arises as the sudden appearance of a localized…