Recovery of a cubic nonlinearity for the nonlinear Schr\"odinger equation
Analysis of PDEs
2023-02-07 v1
Abstract
We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schr\"odinger equation in dimensions two and three. We prove that solutions with data given by small-amplitude wave packets accrue a nonlinear phase that determines the X-ray transform of the nonlinear coefficient.
Keywords
Cite
@article{arxiv.2208.06047,
title = {Recovery of a cubic nonlinearity for the nonlinear Schr\"odinger equation},
author = {Christopher C. Hogan and Jason Murphy and David Grow},
journal= {arXiv preprint arXiv:2208.06047},
year = {2023}
}
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8 pages