A pseudoconformal compactification of the nonlinear Schr "odinger\n equation and applications

2006/06/11 by Terence Tao, Tao, Terence · 3 citations
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0606254

openalex publication_date 2006/06/11 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We interpret the lens transformation (a variant of the pseudoconformal\ntransformation) as a pseudoconformal compactification of spacetime, which\nconverts the nonlinear Schr "odinger equation (NLS) without potential with a\nnonlinear Schr "odinger equation with attractive harmonic potential. We then\ndiscuss how several existing results about NLS can be placed in this\ncompactified setting, thus offering a new perspective to view this theory.\n

Citations

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

Cited by

• Arbitrary norm growth in the 3D Navier-Stokes equations
• The Hartree equation with a constant magnetic field: Well-posedness theory
• On scattering for NLS: rigidity properties and numerical simulations via the lens transform

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