Preprint A423/2005
Well-Posedness for the Schrödinger-Korteweg-de Vries System

Felipe Linares | Corcho , Adan

**Keywords: **
KdV equation | Schrödinger equation

We study well-posedness of the Cauchy problem associated to the
Schrodinger-Korteweg-de Vries system. We obtain local well-posedness for weak
initial data, where the best result obtained is for data in the Sobolev space
$L^2({\R})\times H^{-\tfrac{3}{4}+\delta} $, $0< \delta \le \tfrac{1}{4}$. We also prove global well-posedness
in the energy space $H^1({\R})\times H^1({\R})$. Both results improve considerably the previous ones.