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Related papers: Extreme events in discrete nonlinear lattices

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Using experimental data from three different rogue wave supporting systems, determinism and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the…

Atmospheric and Oceanic Physics · Physics 2015-03-03 Simon Birkholz , Carsten Brée , Ayhan Demircan , Günter Steinmeyer

Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…

Pattern Formation and Solitons · Physics 2007-05-23 Yu. A. Bunyak

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…

Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean…

Optics · Physics 2017-11-22 Akbar Safari , Robert Fickler , Miles J. Padgett , Robert W. Boyd

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves.…

Fluid Dynamics · Physics 2026-04-01 Jie Zhang , Yuxiang Ma , Jiawen Sun , Limin Huang , Michel Benoit , Saulo Mendes

Binary discrete nonlinear Schr\"odinger equation is used to describe dynamics of two-species Bose-Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime…

Pattern Formation and Solitons · Physics 2015-12-10 Denis V. Makarov , M. Yu. Uleysky

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

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

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

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…

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system.…

Exactly Solvable and Integrable Systems · Physics 2017-03-31 Xiao-Yong Wen , Zhenya Yan , Boris A. Malomed

The question of well-posedness of the generalized focusing Ablowitz-Ladik and Discrete Nonlinear Schr\"{o}dinger equations with \textit{nonzero} boundary conditions on the infinite lattice is far less understood than in the case where the…

Analysis of PDEs · Mathematics 2026-03-25 Dirk Hennig , Nikos I. Karachalios , Dionyssios Mantzavinos , Dimitrios Mitsotakis

We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are…

Exactly Solvable and Integrable Systems · Physics 2020-11-09 Abdselam Silem , Hua Wu , Da-jun Zhang

We present a study of the intermittent properties of a shell model of turbulence with unprecedented statistics, about $\sim 10^7$ eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows…

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…

Chaotic Dynamics · Physics 2015-10-06 Sergej Flach

We measure spectra, spatial correlation functions and probability density functions (PDFs) for waves amplitudes for generalized one-dimensional nonlinear Schrodinger (NLS) equation of focusing type with saturated nonlinearity. All…

Optics · Physics 2013-10-18 D. S. Agafontsev

We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically…

Pattern Formation and Solitons · Physics 2026-04-13 Su Yang , Sathyanarayanan Chandramouli , Panayotis G. Kevrekidis

We examine a fractional version of the discrete Nonlinear Schr\"{o}dinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor…

Pattern Formation and Solitons · Physics 2019-11-04 M. I. Molina

Extreme events, or rogue waves, are high-amplitude, rare occurrences that emerge across diverse physical systems and often defy conventional statistical predictions. While optical systems provide a controlled setting for studying these…

Optics · Physics 2026-02-04 T. Wang , Z. Li , Y. Ma , J. Huang , Y. Li , Z. Tu , S. Xiang , G. Ruocco , Y. Hao

The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of…

Pattern Formation and Solitons · Physics 2024-08-22 P. G. Kevrekidis , D. E. Pelinovsky , R. M. Ross