Extreme events in nonlinear lattices

G. P. Tsironis, N. Lazarides, A. Maluckov, Lj Hadžievski

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient structures that can be named as extreme events. We analyze the statistics of the appearance of these collective events in two different universal lattice models; a one-dimensional nonlinear model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrödinger (DNLS) equation, and a two-dimensional disordered DNLS equation. In both cases, extreme events arise in the form of discrete rogue waves as a result of nonlinear interaction and rapid coalescence between mobile discrete breathers. In the former model, we find power-law dependence of the wave amplitude distribution and significant probability for the appearance of extreme events close to the integrable limit. In the latter model, more importantly, we find a transition in the return time probability of extreme events from exponential to power-law regime. Weak nonlinearity and moderate levels of disorder, corresponding to weak chaos regime, favor the appearance of extreme events in that case.

Original languageEnglish
Title of host publicationChaos, Information Processing and Paradoxical Games: The Legacy of John S. Nicolis
PublisherWorld Scientific Publishing Co.
Pages43-62
Number of pages20
ISBN (Electronic)9789814602136
ISBN (Print)9789814602129
DOIs
Publication statusPublished - Jan 1 2014

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ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Cite this

Tsironis, G. P., Lazarides, N., Maluckov, A., & Hadžievski, L. (2014). Extreme events in nonlinear lattices. In Chaos, Information Processing and Paradoxical Games: The Legacy of John S. Nicolis (pp. 43-62). World Scientific Publishing Co.. https://doi.org/10.1142/9789814602136_0003