New York Journal of Mathematics
Volume 15 (2009) 265-282


Terence Tao

A pseudoconformal compactification of the nonlinear Schrödinger equation and applications

Published: June 22, 2009
Keywords: Lens transformation, pseudoconformal NLS, inverse Strichartz theorem
Subject: 35Q55

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.

Author information

Department of Mathematics, UCLA, Los Angeles CA 90095-1555