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A pseudoconformal compactification of the nonlinear Schrödinger equation and applications

Terence Tao
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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.

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Terence Tao. 2009-06-13. A pseudoconformal compactification of the nonlinear Schrödinger equation and applications. https://arxiv.org/abs/math/0606254

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