Extreme events in two-dimensional disordered nonlinear lattices

•We focus on the appearance of extreme events in 2D discrete nonlinear lattices.•Model is based on the Discrete Nonlinear Schrödinger Equation with quenched disorder.•The extreme event appearance probability and time-statistics are considered.•Work is motivated from experimental studies in evanescently coupled optical fibers.

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.

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