  An efficient high precision hybrid numerical approach for
  integrable Davey-Stewartson (DS) I equations for trivial boundary conditions
at infinity is presented for
  Schwartz class initial data. The code is used for a detailed numerical study
of DS I solutions in this class. Localized stationary solutions are constructed
and shown to be unstable against dispersion and blow-up. A finite-time blow-up
of initial data in the Schwartz class of smooth rapidly decreasing functions is
discussed.
