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Related papers: Time-Reversal Generation of Rogue Waves

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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

Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects…

Fluid Dynamics · Physics 2012-08-21 L. H. Ying , L. Kaplan

The nonlinear Schr\"odinger equation (NLSE) models the slowly varying envelope dynamics of a weakly nonlinear quasi-monochromatic wave packet in dispersive media. In the context of Bose-Einstein condensate (BEC), it is often referred to as…

Pattern Formation and Solitons · Physics 2019-12-24 N. Karjanto

The the mixed Chen-Lee-Liu derivative nonlinear Schr\"odinger equation (CLL-NLS) can be considered as simplest model to approximate the dynamics of weakly nonlinear and dispersive waves, taking into account the self-steepnening effect…

Exactly Solvable and Integrable Systems · Physics 2015-05-12 Yongshuai Zhang , Lijuan Guo , Amin Chabchoub , Jingsong He

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…

Pattern Formation and Solitons · Physics 2009-11-13 Juan Belmonte-Beitia , Victor M. Perez-Garcia , Vadym Vekslerchik , Vladimir V. Konotop

We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude…

Soft Condensed Matter · Physics 2009-11-10 Z. Rapti , P. G. Kevrekidis , A. Smerzi , A. R. Bishop

From among the waves whose dynamics are governed by the nonlinear Schr\"odinger (NLS) equation, we find a robust, spatiotemporally disordered family, in which waves initialized with increasing amplitudes, on average, over long time scales,…

Pattern Formation and Solitons · Physics 2021-07-05 Katelyn Plaisier Leisman , Douglas Zhou , J. W. Banks , Gregor Kovačič , David Cai

We start from the remark that in wave turbulence theory, exemplified by the cubic twodimensional Schr{\"o}dinger equation (NLS) on the real plane, the regularity of the resonant manifold is linked with dispersive properties of the equation…

Analysis of PDEs · Mathematics 2023-07-06 Erwan Faou , Antoine Mouzard

Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrodinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much…

Fluid Dynamics · Physics 2017-03-17 Alexey Slunyaev , Anna Sergeeva , Efim Pelinovsky

The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…

Fluid Dynamics · Physics 2015-11-03 Y. Charles Li

In the present investigation, the solutions on the periodic and double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the…

Exactly Solvable and Integrable Systems · Physics 2021-11-30 H. J. Zhou , Y. Chen

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

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

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 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

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

We consider the nonlinear Schr\"odinger (NLS) equation posed on the box $[0,L]^d$ with periodic boundary conditions. The aim is to describe the long-time dynamics by deriving effective equations for it when $L$ is large and the…

Analysis of PDEs · Mathematics 2016-10-13 Tristan Buckmaster , Pierre Germain , Zaher Hani , Jalal Shatah

Being considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schr\"odinger equation (NLS) has been recently observed and intensely investigated experimentally in particular…

Fluid Dynamics · Physics 2015-06-16 A. Chabchoub , N. Hoffmann , H. Branger , C. Kharif , N. Akhmediev

By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time…

Exactly Solvable and Integrable Systems · Physics 2019-03-05 Xi-Zhong Liu