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Related papers: Extreme waves statistics for Ablowitz-Ladik system

200 papers

Time evolution equation for the Probability Distribution Function (PDF) is derived for system of weakly interacting waves. It is shown that a steady state for such system may correspond to strong intermittency.

Mathematical Physics · Physics 2009-11-10 Yeontaek Choi , Yuri V. Lvov , Sergey Nazarenko , Boris Pokorni

The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional non- linear model with deep-water waves dispersion relation,…

Chaotic Dynamics · Physics 2015-01-22 Will Cousins , Themistoklis P. Sapsis

We investigate the statistical mechanics of the photonic Ablowitz-Ladik lattice, the integrable version of the discrete nonlinear Schr\"odinger equation. In this regard, we demonstrate that in the presence of perturbations the complex…

We develop a general analytical framework for determining the probability distribution of random nonlinear wave fields governed by the focusing nonlinear Schr\"odinger equation (fNLSE) in regimes where typical realizations are dominated by…

Pattern Formation and Solitons · Physics 2026-05-08 T. Congy , G. A. El

Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of…

Strongly Correlated Electrons · Physics 2023-03-29 O. Cépas , P. Quémerais

We study a one-dimensional discrete nonlinear Schr\"odinger model with hopping to the first and a selected N-th neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability…

Quantum Gases · Physics 2016-06-10 J. Stockhofe , P. Schmelcher

The interaction between two co-propagating electrostatic wavepackets characterized by arbitrary carrier wavenumber is considered. A one-dimensional (1D) non-magnetized plasma model is adopted, consisting of a cold inertial ion fluid…

Plasma Physics · Physics 2024-03-26 N. Lazarides , Giorgos P. Veldes , Amaria Javed , Ioannis Kourakis

We study numerically the statistical properties of the modulation instability (MI) developing from condensate solution seeded by weak, statistically homogeneous in space noise, in the framework of the classical (integrable) one-dimensional…

Exactly Solvable and Integrable Systems · Physics 2014-08-04 D. S. Agafontsev , V. E. Zakharov

We study the evolution of localized wave groups in unidirectional water wave envelope equations (nonlinear Schrodinger (NLS) and modified NLS (MNLS)). These localizations of energy can lead to disastrous extreme responses (rogue waves).…

Pattern Formation and Solitons · Physics 2015-01-22 Will Cousins , Themistoklis P. Sapsis

A hydrodynamical description of coherent instabilities that take place in the longitudinal dynamics of a charged-particle coasting beam in a high-energy accelerating machine is presented. This is done in the framework of the Madelung fluid…

Accelerator Physics · Physics 2009-11-11 R. Fedele , D. Anderson , M. Lisak

We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are quasi-periodic…

Chaotic Dynamics · Physics 2007-05-23 Lutz Brusch , Alessandro Torcini , Markus Baer

The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of…

Statistical Mechanics · Physics 2011-09-14 Claudio Conti , Luca Leuzzi

We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled…

Other Condensed Matter · Physics 2009-11-11 Kenichi Kasamatsu , Makoto Tsubota

The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of…

Computational Physics · Physics 2020-06-17 Claire David , Pierre Sagaut

Mean-filed dynamics of a Bose-Einstein condensate (BEC) loaded in an optical lattice (OL), confined by a parabolic potentials, and subjected to change of a scattering length by means of the Feshbach resonance (FR), is considered. The system…

Soft Condensed Matter · Physics 2009-11-10 V. A. Brazhnyi , V. V. Konotop

The modulational instability of waves in a medium under the action of an external monochromatic force and dissipation is considered. The model which describes the nonlinear stage of the modulation instability was constructed with using…

Pattern Formation and Solitons · Physics 2012-11-29 Evgeny Belkin , Alexander Kirichok , Vladimir Kuklin

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 Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localised solitons to rational solutions in the form of the spatiotemporally localised…

Pattern Formation and Solitons · Physics 2022-05-04 Dirk Hennig , Nikos I. Karachalios , Jesus Cuevas-Maraver

Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves - a seminal framework for studying the unstable growth of finite…

Atmospheric and Oceanic Physics · Physics 2026-04-16 Nicolas De Ro , Jonathan Demaeyer , Stéphane Vannitsem

Modulational, Benjamin-Feir, instability is studied for the down-stream evolution of surface gravity waves. An explicit solution, the soliton on finite background, of the NLS equation in physical space is used to study various phenomena in…

Fluid Dynamics · Physics 2019-06-03 Andonowati , N. Karjanto , E. van Groesen