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Related papers: Rogue waves in nonlocal media

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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

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 study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrodinger equation (NLSE) extended by R.…

Chaotic Dynamics · Physics 2015-12-14 Cihan Bayindir

In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable…

Exactly Solvable and Integrable Systems · Physics 2015-09-15 D. S. Agafontsev , V. E. Zakharov

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 Zhenya Yan

The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue…

Exactly Solvable and Integrable Systems · Physics 2018-05-01 P. G. Grinevich , P. M. Santini

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 present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…

Exactly Solvable and Integrable Systems · Physics 2013-01-08 Nikolay K. Vitanov , Amin Chabchoub , Norbert Hoffmann

General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the…

Exactly Solvable and Integrable Systems · Physics 2015-05-30 Yasuhiro Ohta , Jianke Yang

In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schr\"odinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue…

Analysis of PDEs · Mathematics 2021-11-16 Miguel Angel Garrido , Ricardo Grande , Kristin M. Kurianski , Gigliola Staffilani

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

We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…

Pattern Formation and Solitons · Physics 2014-10-23 J. S. He , E. G. Charalampidis , P. G. Kevrekidis , D. J. Frantzeskakis

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 construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave…

Pattern Formation and Solitons · Physics 2021-08-31 N. Sinthuja , K. Manikandan , M. Senthilvelan

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

The spatially periodic breather solutions (SPBs) of the nonlinear Schr\"odinger equation, prominent in modeling rogue waves, are unstable. In this paper we numerically investigate the effects of nonlinear dissipation and higher order…

Pattern Formation and Solitons · Physics 2022-06-15 C. M. Schober , A. Islas

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection…

Fluid Dynamics · Physics 2022-06-22 Yuchen He , Andy Witt , Stefano Trillo , Amin Chabchoub , Norbert Hoffmann

We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…

Exactly Solvable and Integrable Systems · Physics 2014-07-23 Fabio Baronio , Matteo Conforti , Antonio Degasperis , Sara Lombardo , Miguel Onorato , Stefan Wabnitz

Supratransmission is a fascinating and counterintuitive nonlinear wave phenomenon that enables energy transmission through frequency band gaps. Recent studies have suggested that supratransmission in a damped-driven Klein-Gordon equation…

Pattern Formation and Solitons · Physics 2025-04-29 Abrari Noor Hasmi , Hadi Susanto