11-137 Alexei Rybkin

Korteweg-de Vries equation, inverse scattering transform, Schr dinger operator, Hankel operator, Gevrey regularity. (113K, LaTeX with bib file) Sep 27, 11

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Abstract. We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles q's which are, in a certain sense, essentially bounded from below and q(x)=O(e^{-cx^{ }}),x + , with some positive c and . Using the inverse scattering transform, we show that the KdV flow turns such initial data into a function which is (1) meromorphic (in the space variable) on the whole complex plane if >1/2, (2) meromorphic on a strip around the real line if =1/2, and (3) Gevrey regular if <1/2. Note that q's need not have any decay or pattern of behavior at - .

Files: 11-137.src( 11-137.keywords , bibryb.bib , merom2011-10.tex )