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Related papers: Rogue waves, self-similar statistics, and self-sim…

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Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the Rogue waves are localized surface waves, their theoretical models and experimental…

Exactly Solvable and Integrable Systems · Physics 2015-03-13 Anjan Kundu , Abhik Mukherjee , Tapan Naskar

We propose an alternative to the standard mechanisms for the formation of rogue waves in a non-conservative, nonlinear lattice dynamical system. We consider an ODE system that features regular periodic bursting arising from forced symmetry…

Pattern Formation and Solitons · Physics 2022-08-17 Priya Subramanian , Edgar Knobloch , P. G. Kevrekidis

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…

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…

Exactly Solvable and Integrable Systems · Physics 2021-06-09 Jinbing Chen , Dmitry E. Pelinovsky

We consider the asymptotic behavior of the solutions of a nonlinear Schr\"odinger (NLS) model incorporating linear and nonlinear gain/loss. First, we describe analytically the dynamical regimes (depending on the gain/loss strengths), for…

Pattern Formation and Solitons · Physics 2017-06-14 Z. A. Anastassi , G. Fotopoulos , D. J. Frantzeskakis , T. P. Horikis , N. I. Karachalios , P. G. Kevrekidis , I. G. Stratis , K. Vetas

A hydrodynamic model of active, low Reynolds number suspensions, shows the emergence of an asymptotic state with a universal spectral scaling and non-Gaussian (intermittent) fluctuations in the velocity field. Such states arise when these…

Fluid Dynamics · Physics 2023-06-28 Siddhartha Mukherjee , Rahul K. Singh , Martin James , Samriddhi Sankar Ray

Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…

Chaotic Dynamics · Physics 2015-06-17 Jakob J. Metzger , Ragnar Fleischmann , Theo Geisel

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…

Exactly Solvable and Integrable Systems · Physics 2014-07-14 K. Manikandan , M. Senthilvelan

Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and…

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

An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…

Quantum Physics · Physics 2011-08-02 Arul Lakshminarayan , Steven Tomsovic , Oriol Bohigas , Satya N. Majumdar

In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…

Optics · Physics 2021-05-26 Éva Rácz , László Ruppert , Radim Filip

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

Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow…

Fluid Dynamics · Physics 2025-02-07 Saulo Mendes , Yuchen He , Jérôme Kasparian , Amin Chabchoub

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical…

Fluid Dynamics · Physics 2019-04-04 Alexey Slunyaev , Anna Kokorina

We present a statistical analysis based on the height and return time probabilities of high amplitude wave events in both focusing and defocusing Manakov systems. We find that analytical rational/semirational solutions, associated with…

Pattern Formation and Solitons · Physics 2018-08-01 A. Mancic , F. Baronio , Lj. Hadzievski , S. Wabnitz , A. Maluckov

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with…

Pattern Formation and Solitons · Physics 2012-04-12 Stefano Lepri , Giulio Casati

The efforts to understand the physics of rogue waves have motivated the study of mechanisms that produce rare, extreme events, often through analogous optical setups. As many studies have reported nonlinear generation mechanisms, recent…

This paper delves into the study of multi-component derivative nonlinear Schrodinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation (DT) method, we derive higher-order vector rogue wave…

Exactly Solvable and Integrable Systems · Physics 2023-12-20 Lin Huian , Ling Liming

We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrodinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially…

Exactly Solvable and Integrable Systems · Physics 2019-09-25 Giacomo Roberti , Gennady El , Stephane Randoux , Pierre Suret