The Cauchy problem for a Schroedinger - Korteweg - de Vries system with   rough data
  The Cauchy problem for a coupled system of the Schroedinger and the KdV equation is shown to be globally well-posed for data with infinite energy. The proof uses refined bilinear Strichartz estimates and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao. 
Hartmut Pecher