Extreme events in discrete nonlinear lattices

Abstract

We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.

5 pages, 4 figures; reference added, figure 2 corrected

References in corpus (10)

• Discrete Breathers
• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Freak Waves in Random Oceanic Sea States
• Harnessing and control of optical rogue waves in supercontinuum generation
• Localized States in Discrete Nonlinear Schrödinger Equations
• Instability and Evolution of Nonlinearly Interacting Water Waves
• Discrete Nonlinear Schr{ö}dinger Breathers in a Phonon Bath
• Localization and Coherence in Nonintegrable Systems
• Discrete Solitons in the Salerno Model with competing nonlinearities
• Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves

Cited by in corpus (11)

• Wave packet dynamics in chains with delayed electronic nonlinear response
• Extreme waves and branching flows in optical media
• Extreme events in two dimensional disordered nonlinear lattices
• Effect of quintic nonlinearity on modulation instability in coupled nonlinear Schroedinger systems
• Spatial rogue waves in photorefractive SBN crystals
• Extreme waves statistics for Ablowitz-Ladik system
• Statistics of Vector Manakov Rogue Waves
• Extreme events due to localisation of energy
• Rogue waves, self-similar statistics, and self-similar intermediate asymptotics
• Extreme Events in Nonlinear Lattices
• Waves statistics for generalized one-dimensional Nonlinear Schrodinger Equation with saturated nonlinearity