Existence of pseudo-conformally invariant solutions to the Davey-Stewartson system

We prove that the pseudo-conformal group of the Schrodinger equation acts o n solutions of the Davey Stewartson system and that there exists an infinit e family of solutions which are invariant under the action of that group. W e also exhibit two different time behaviors for these invariant solutions o f the Davey-Stewartson system, and we study the stability of some of these solutions, and prove that initial data close to them give rise to global so lutions asymptotically behaving like an invariant solution. (C) 2001 Academ ic Press.