The scattering map determines the nonlinearity
Killip R, Murphy J, Vişan M. 2023. The scattering map determines the nonlinearity. Proceedings of the American Mathematical Society. 151(6), 2543–2557.
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Author
Killip, Rowan;
Murphy, Jason;
Vişan, MonicaISTA
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.
Mathematics Subject Classification
Publishing Year
Date Published
2023-06-01
Journal Title
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society
Volume
151
Issue
6
Page
2543-2557
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Murphy J, Vişan M. The scattering map determines the nonlinearity. Proceedings of the American Mathematical Society. 2023;151(6):2543-2557. doi:10.1090/proc/16297
Killip, R., Murphy, J., & Vişan, M. (2023). The scattering map determines the nonlinearity. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/16297
Killip, Rowan, Jason Murphy, and Monica Vişan. “The Scattering Map Determines the Nonlinearity.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/16297.
R. Killip, J. Murphy, and M. Vişan, “The scattering map determines the nonlinearity,” Proceedings of the American Mathematical Society, vol. 151, no. 6. American Mathematical Society, pp. 2543–2557, 2023.
Killip R, Murphy J, Vişan M. 2023. The scattering map determines the nonlinearity. Proceedings of the American Mathematical Society. 151(6), 2543–2557.
Killip, Rowan, et al. “The Scattering Map Determines the Nonlinearity.” Proceedings of the American Mathematical Society, vol. 151, no. 6, American Mathematical Society, 2023, pp. 2543–57, doi:10.1090/proc/16297.
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