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SUMMARY:Solving Nonlinear Dispersive Equations in Dimension Two by the Met
 hod of Inverse Scattering - Perry\, P (University of Kentucky)
DTSTART:20111108T140000Z
DTEND:20111108T150000Z
UID:TALK34492@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The Davey-Stewartson II equation and the Novikov-Veselov equat
 ions are nonlinear dispersive equations in two dimensions\, respectively d
 escribing the motion of surface waves in shallow water and geometrical opt
 ics in nonlinear media. Both are integrable by the $overline{partial}}$-me
 thod of inverse scattering\, and may be onsidered respective analogues of 
 the cubic nonlinear Schrodinger equation and the KdV equation in one dimen
 sion. We will prove global well-posedness for the defocussing DS II equati
 on in the space $H^{1\,1}(R^2}$ consisting of $L^2$ functions with $\nabla
  u$ and $(1+|\, ot \,|) u(\, ot \, )$ square-integrable. Using the same 
 scattering and inverse scattering maps\, we will also show that the invers
 e scattering method yields global\, smooth solutions of the Novikov-Veselo
 v equation for initial data of conductivity type\, solving an open problem
  posed recently by Lassas\, Mueller\, Siltanen\, and Stahel.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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