English

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}
}

Comments

8 pages