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.
C. C. Hogan et al., "Recovery of a Cubic Nonlinearity for the Nonlinear Schrödinger Equation," Journal of Mathematical Analysis and Applications, vol. 522, no. 1, article no. 127016, Elsevier, Jun 2023.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2023.127016
Mathematics and Statistics
Keywords and Phrases
Inverse Problem; NLS
International Standard Serial Number (ISSN)
Article - Journal
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01 Jun 2023