BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Stochastic nonlinear Schrodinger equations and modulation of solit
 ary waves - de Bouard\, A (cole Polytechnique)
DTSTART:20100122T113000Z
DTEND:20100122T123000Z
UID:TALK22657@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We focus on the asymptotic behavior of the solution of a model
  equation for Bose-Einstein condensation\, in the case where the trapping 
 potential varies randomly in time.\n\nThe model is the so called Gross-Pit
 aevskii equation\, with a quadratic potential with white noise fluctuation
 s in time whose amplitude tends to zero.\n\nThe initial condition is a sta
 nding wave solution of the unperturbed equation.\nWe prove that up to time
 s of the order of the inverse squared amplitude the solution decomposes in
 to the sum of a randomly modulated standing wave and a small remainder\, a
 nd we derive the equations for the modulation parameters.\n\nIn addition\,
  we show that the first order of the remainder\, as the noise amplitude go
 es to zero\, converges to a Gaussian process\, whose expected mode amplitu
 des concentrate on the third eigenmode generated by the Hermite functions\
 , on a certain time scale\, as the frequency of the standing wave of the d
 eterministic equation tends to its minimal value.\n
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR