---
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\left( x\right) =O\left(
    e^{-cx^{\varepsilon }}\right) ,x\rightarrow +\infty $, with some positive $c$ and $\varepsilon $. 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 $\varepsilon >1/2$, (2) meromorphic on a strip around the real line if $\varepsilon =1/2$, and (3) Gevrey regular if $\varepsilon <1/2$. Note that $q$’s need not have any decay or pattern of behavior at $-\infty $.
address:
- University of Alaska Fairbanks
- |
    Department of Mathematics and Statistics\
    University of Alaska Fairbanks\
    PO Box 756660\
    Fairbanks, AK 99775
author:
- Alexei Rybkin
bibliography:
- 'bibryb.bib'
date: 'September, 2011'
title: 'Spatial Analyticity of solutions to integrable systems. I. The KdV case'
---

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Introduction and statements of main results
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The gain and persistence of regularity effects are important features of many dispersive (linear and nonlinear) partial differential equations (PDEs). The literature on the subject is truly enormous and we make 