Extreme events in two dimensional disordered nonlinear lattices

Abstract

Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as well as persistent localized structures, some of which have extreme magnitude. We analyze the statistics of occurrence of these extreme collective events and find that the appearance of transient extreme events is more likely in the weakly nonlinear regime. We observe a transition in the extreme events recurrence time probability from exponential, in the nonlinearity dominated regime, to power law for the disordered one.

5 figures, 5 pages

References in corpus (10)

• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Harnessing and control of optical rogue waves in supercontinuum generation
• Non-Gaussian statistics and extreme waves in a nonlinear optical cavity
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Recurrence time analysis, long-term correlations, and extreme events
• Triggering rogue waves in opposing currents
• Return interval distribution of extreme events and long term memory
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• Extreme events in discrete nonlinear lattices

Cited by in corpus (7)

• Intermittent large deviation of chaotic trajectory in Ikeda map: Signature of extreme events
• Extreme waves and branching flows in optical media
• Rogue and solitary waves in coupled phononic crystals
• Discrete Rogue waves in an array of waveguides
• Statistics of Vector Manakov Rogue Waves
• Extreme events due to localisation of energy
• Extreme Events in Nonlinear Lattices