Determination of Schrödinger nonlinearities from the scattering map

2024/02/05 by Killip, Rowan, Murphy, Jason, Visan, Monica · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.03218

Abstract

We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schrödinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schrödinger solutions. We then solve this deconvolution problem using the Beurling--Lax Theorem.

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• On scattering for NLS: rigidity properties and numerical simulations via the lens transform

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