A pseudoconformal compactification of the nonlinear Schr\"odinger equation and applications
Analysis of PDEs
2009-06-13 v4
Abstract
We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schr\"odinger equation (NLS) without potential with a nonlinear Schr\"odinger 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.
Cite
@article{arxiv.math/0606254,
title = {A pseudoconformal compactification of the nonlinear Schr\"odinger equation and applications},
author = {Terence Tao},
journal= {arXiv preprint arXiv:math/0606254},
year = {2009}
}
Comments
17 pages, no figures, to appear, New York J. Math. This is the final version