THE SCATTERING MAP DETERMINES THE NONLINEARITY

Author

Rowan Killip
Jason Murphy, Missouri University of Science and TechnologyFollow
Monica Visan

Abstract

Using the two-dimensional nonlinear Schrödinger equation as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under very mild assumptions on the nonlinearity, the wave operator uniquely determines the nonlinearity, as does the scattering map. Evaluating the scattering map on well-chosen initial data, we reduce the problem to an inverse convolution problem, which we solve by means of an application of the Beurling–Lax Theorem.

Recommended Citation

R. Killip et al., "THE SCATTERING MAP DETERMINES THE NONLINEARITY," Proceedings of the American Mathematical Society, vol. 151, no. 6, pp. 2543 - 2557, American Mathematical Society, Jun 2023.

The definitive version is available at https://doi.org/10.1090/proc/16297

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant 2137217

International Standard Serial Number (ISSN)

1088-6826; 0002-9939

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 American Mathematical Society, All rights reserved.

Publication Date

01 Jun 2023