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SUMMARY:Exit times and persistence of solitons for a stochastic Korteweg-d
 e Vries Equation - Gautier\, E (ENSAE)
DTSTART:20100329T153000Z
DTEND:20100329T163000Z
UID:TALK23988@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Solitons constitute a two parameters family of particular solu
 tion to the Korteweg-de Vries (KdV) equation. They are progressive localiz
 ed waves that propagate with constant speed and shape. They are stable in 
 many ways against perturbations or interactions. We consider the stability
  with respect to random perturbations by an additive noise of small amplit
 ude. It has been proved by A. de Bouard and A. Debussche that originating 
 from a soliton profile\, the solution remains close to a soliton with rand
 omly fluctuating parameters. We revisit exit times from a neighborhood of 
 the deterministic soliton and randomly fluctuating solitons using large de
 viations. This allows to quantify the time scales on which such approximat
 ions hold and the gain obtained by eliminating secular modes in the study 
 of the stability.
LOCATION:Seminar Room 1\, Newton Institute
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