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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

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 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 defocusing nonlinear Schr\"odinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in…

Pattern Formation and Solitons · Physics 2021-11-19 Li Wang , Zhenya Yan

The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…

Pattern Formation and Solitons · Physics 2017-04-26 Theodoros P. Horikis , Mark J. Ablowitz

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

We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time (PT)-symmetric system of linearly-coupled nonlinear…

Optics · Physics 2013-07-17 Yu. V. Bludov , R. Driben , V. V. Konotop , B. A. Malomed

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

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

Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schr\"odinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics and plasmas, exhibits…

Pattern Formation and Solitons · Physics 2016-01-07 H. N. Chan , B. A. Malomed , K. W. Chow , E. Ding

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

Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schr\"odinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general…

Pattern Formation and Solitons · Physics 2016-11-23 Marco Bertola , Gennady El , Alexander Tovbis

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

In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of…

Exactly Solvable and Integrable Systems · Physics 2013-04-10 Yongshuai Zhang , Lijuan Guo , Shuwei Xu , Zhiwei Wu , Jingsong HE

We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The…

Exactly Solvable and Integrable Systems · Physics 2019-10-15 Bao-Feng Feng , Liming Ling , Daisuke A. Takahashi

Rogue waves in birefringent optical fibers are analyzed within the framework of the coupled nonlinear Schr\"odinger (CNLS) system. The generation of rogue waves is frequently associated with modulation instability (MI). It is commonly…

Pattern Formation and Solitons · Physics 2016-07-08 Mark J. Ablowitz , Theodoros P. Horikis

The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schr\"odinger (MNLS) equation in one spatial-dimension with random initial conditions that are assumed to be normally distributed, with a spectrum…

Fluid Dynamics · Physics 2018-01-24 Giovanni Dematteis , Tobias Grafke , Eric Vanden-Eijnden

Breathers and rogue waves of special coupled nonlinear Schr\"odinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence.…

Pattern Formation and Solitons · Physics 2014-10-29 Jin Hua Li , Hiu Ning Chan , Kin Seng Chiang , Kwok Wing Chow

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

A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…

Pattern Formation and Solitons · Physics 2019-03-27 Abhik Mukherjee , Anjan Kundu