arXiv:math/0606254 Abstract

arXiv:math/0606254 [math.AP]Abstract References Reviews Resources

A pseudoconformal compactification of the nonlinear Schrödinger equation and applications

Published 2006-06-11, updated 2009-06-13Version 4

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.

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

Categories: math.AP

Subjects: 35Q55

Keywords: nonlinear schrödinger equation, pseudoconformal compactification, applications, lens transformation, pseudoconformal transformation

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