A pseudoconformal compactification of the nonlinear Schrödinger equation and applications

Details A pseudoconformal compactification of the nonlinear Schrödinger equation and applications A pseudoconformal compactification of the nonlinear Schrödinger equation and applications

2006-06-11

arxiv.org/abs/math/0606254v4

Mathematics

Analysis of PDEs

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

Scientific paper

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.

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