Solving Nonlinear Dispersive Equations in Dimension Two by the Method of Inverse Scattering

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• Perry, P (University of Kentucky)
• Tuesday 08 November 2011, 14:00-15:00
• Seminar Room 2, Newton Institute Gatehouse.

If you have a question about this talk, please contact Mustapha Amrani.

Inverse Problems

The Davey-Stewartson II equation and the Novikov-Veselov equations are nonlinear dispersive equations in two dimensions, respectively describing the motion of surface waves in shallow water and geometrical optics in nonlinear media. Both are integrable by the $overline{partial}}$-method of inverse scattering, and may be onsidered respective analogues of the cubic nonlinear Schrodinger equation and the KdV equation in one dimension. We will prove global well-posedness for the defocussing DS II equation in the space $H^(R2}$ consisting of $L^2$ functions with $ abla u$ and $(1+|, ot ,|) u(, ot , )$ square-integrable. Using the same scattering and inverse scattering maps, we will also show that the inverse scattering method yields global, smooth solutions of the Novikov-Veselov equation for initial data of conductivity type, solving an open problem posed recently by Lassas, Mueller, Siltanen, and Stahel.

This talk is part of the Isaac Newton Institute Seminar Series series.

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