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Extreme events are characterised by low probabilities and high impact on the systems. As a consequence, it is possible to find many studies about the predictability and suppression of extreme events. In this work, we show the existence of dragon-kings extreme events in nonlinear three-wave interactions. Dragon-king extreme events, identified by phase transitions, tipping points, and catastrophes, affects fluctuating systems. We show that these events can be avoided by adding a perturbing small amplitude wave to the system.
This introductory article presents the special Discussion and Debate volume From black swans to dragon-kings, is there life beyond power laws? published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contribution
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a functio
We provide, and perform a risk theoretic statistical analysis of, a dataset that is 75 percent larger than the previous best dataset on nuclear incidents and accidents, comparing three measures of severity: INES (International Nuclear Event Scale), r
Via a sequence of approximations of the Lagrangian in Hamiltons principle for dispersive nonlinear gravity waves we derive a hierarchy of Hamiltonian models for describing wave-current interaction (WCI) in nonlinear dispersive wave dynamics on free s
The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of generating function and of multi-point pdf, for weakly interacting waves with initial random phases. When also initial amplitudes are random, the one-po