Abstract
We consider the analytic smoothing effect for the KdV equation. That is to say, if the initial data given at $t = 0$ decays very rapidly, the solution to the Cauchy problem becomes analytic with respect to the space variable for $t > 0$. In this paper we show this effect by using the inverse scattering method which transforms the KdV equation to a linear dispersive equation whose analytic smoothing effect is shown through the properties of the Airy function.
Citation
Shigeo Tarama. "Analyticity of solutions of the Korteweg-de Vries equation." J. Math. Kyoto Univ. 44 (1) 1 - 32, 2004. https://doi.org/10.1215/kjm/1250283580
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