A pseudoconformal compactification of the nonlinear Schrödinger equation and applications

Abstract

We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schrödinger equation (NLS) without potential with a nonlinear Schrödinger equation with attractive harmonic potential. We then discuss how several existing results about NLS can be placed in this compactified setting, thus offering a new perspective to view this theory.

17 pages, no figures, to appear, New York J. Math. This is the final version