Dresden 2014 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Nonlinear Stochastic Systems

DY 10.5: Talk

Tuesday, April 1, 2014, 10:30–10:45, ZEU 160

Ultar-long-tail simulation and modelling of rogue wave statistics — Marc Eberhard¹, •Rudolf A. Römer², and Akihiro Maruta³ — ¹Aston University, Birmingham, B4 7ET — ²University of Warwick, Coventry CV4 7AL, UK — ³Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Optical "rogue waves" generated in fiber systems are sharp, rare and extremely high power pulses that share the main features of the devastating freak waves appearing in the ocean. In fact, rogue waves are known to occur also in plasmas, Bose-Einstein condensates and super-fluid helium. Rogue waves are argued to to form due to at least two mechanisms of amplification. First, a modulation instability broadens the power spectrum of the waves - and hence "amplifies" waves in frequency ranges where there were none to start with. The second amplification is then due to multiple inelastic soliton collisions. In order to describe rogue waves quantitatively, it has been shown that their probability density function depicts a typical 'L-shaped' profile, characterizing the occurrence of many small events as well as, in the horizontal part of the 'L', some very rare and extremely powerful events. What drives the formation of this 'L'-shaped PDF is not yet clear. Recently, it was argued that a third-order dispersion term might be responsible. A remarkable feature of the third-order dispersion is that the energy of the stronger soliton in most of the cases increases after the collision. Hence after multiple such collisions, the strongest soliton will have accumulated most of the energy in the system, it has become a rogue wave!