THE STRUCTURE OF SOLUTIONS TO THE PSEUDOCONFORMALLY INVARIANT NONLINEAR SCHRODINGER-EQUATION

We study solutions in R(n) of the nonlinear Schrodinger equation iu(t) + DELTA-u = lambda\u\gamma-u, where gamma is the fixed power 4/n. For this particular power, these solutions satisfy the "pseudo-conformal" conservation law, and the set of solutions is invariant under a related transformation. This transformation gives a correspondence between global and non-global solutions (if lambda < 0), and therefore allows us to deduce properties of global solutions from properties of non-global solutions, and vice versa. In particular, we show that a global solution is stable if and only if it decays at the same rate as a solution to the linear problem (with lambda = 0). Also, we obtain an explicit formula for the inverse of the wave operator; and we give a sufficient condition (if lambda < 0) that the blow up time of a non-global solution is a continuous function on the set of initial values with (for example) negative energy.