Recovery of a Cubic Nonlinearity for the Nonlinear Schrödinger Equation

Author

Christopher C. Hogan
Jason Murphy, Missouri University of Science and TechnologyFollow
David E. Grow, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

Inverse Problem; NLS

International Standard Serial Number (ISSN)

1096-0813; 0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Elsevier, All rights reserved.

Publication Date

01 Jun 2023