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SUMMARY:Statistics of Extreme Events in Integrable Turbulence - Thibault C
 ongy (Northumbria University)
DTSTART:20221020T133000Z
DTEND:20221020T140000Z
UID:TALK182588@talks.cam.ac.uk
DESCRIPTION:Integrable turbulence has proven to be a successful framework 
 to describe random nonlinear waves in integrable dynamics such as the focu
 sing nonlinear Schr&ouml\;dinger (fNLS) equation. The soliton gas\, which 
 can be seen as a stochastic ensemble of interacting solitons\, constitutes
  one of the fundamental cases of integrable turbulence. We investigate in 
 this work the likelihood of extreme events for a soliton gas of the fNLS e
 quation\, by computing analytically the kurtosis of the solution wave ampl
 itude.The theory is illustrated by physically relevant examples of dense s
 oliton gas. We first consider the asymptotic development of the noise indu
 ced modulational instability of the fNLS equation\, which can be modeled b
 y a bound state soliton gas. We then extend the result to the more general
  problem of the evolution of partially coherent waves\, corresponding to s
 tochastic initial conditions with slowly varying amplitude. For each examp
 le\, the analytical formula of the kurtosis successfully compares to the v
 alue obtained with the numerical implementation of the problem.This is a j
 oint work with G. El\, S. Randoux\, G. Roberti\, P. Suret and A. Tovbis.
LOCATION:Seminar Room 1\, Newton Institute
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