Determination of Schr\"odinger nonlinearities from the scattering map
Analysis of PDEs
2025-09-19 v1
Abstract
We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schr\"odinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schr\"odinger solutions. We then solve this deconvolution problem using the Beurling--Lax Theorem.
Cite
@article{arxiv.2402.03218,
title = {Determination of Schr\"odinger nonlinearities from the scattering map},
author = {Rowan Killip and Jason Murphy and Monica Visan},
journal= {arXiv preprint arXiv:2402.03218},
year = {2025}
}
Comments
18 pages