Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation

Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation

We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schrödinger equation in dimensions d≥2. 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.

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Veröffentlicht in:Journal of mathematical analysis and applications 2023-06, Vol.522 (1), p.127016, Article 127016
Hauptverfasser: Hogan, Christopher C., Murphy, Jason, Grow, David
Format: Artikel
Sprache:eng
Schlagworte:
Inverse problem
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Zusammenfassung:We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schrödinger equation in dimensions d≥2. 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127016