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Michael Taylor, University of North Carolina
Short Time Behavior of Solutions to Nonlinear Schrodinger Equations
We examine the fine structure of the short time behavior of solutions to certain nonlinear Schrodinger equations, with emphasis on cases where the initial data are piecewise smooth, with jump discontinuity, on Euclidean space of dimension one or two. We analyze Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon, which first arose in the study of Fourier inversion.