Extreme events in discrete nonlinear lattices

Details Extreme events in discrete nonlinear lattices Extreme events in discrete nonlinear lattices

2009-01-22

arxiv.org/abs/0901.3480v2

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1103/PhysRevE.79.025601

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.

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