Existence of Pseudo-Conformally Invariant Solutions to the Davey–Stewartson System

We prove that the pseudo-conformal group of the Schrödinger equation acts on solutions of the Davey–Stewartson system and that there exists an infinite family of solutions which are invariant under the action of that group. We also exhibit two different time behaviors for these invariant solutions of 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 solutions asymptotically behaving like an invariant solution