Determination of Schrödinger nonlinearities from the scattering map
Killip R, Murphy J, Vişan M. 2025. Determination of Schrödinger nonlinearities from the scattering map. Nonlinearity. 38(1), 015021.
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Author
Killip, Rowan;
Murphy, Jason;
Vişan, MonicaISTA
Abstract
We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schrödinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schrödinger solutions. We then solve this deconvolution problem using the Beurling–Lax Theorem.
Publishing Year
Date Published
2025-01-01
Journal Title
Nonlinearity
Publisher
IOP Publishing
Volume
38
Issue
1
Article Number
015021
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Murphy J, Vişan M. Determination of Schrödinger nonlinearities from the scattering map. Nonlinearity. 2025;38(1). doi:10.1088/1361-6544/ada1bf
Killip, R., Murphy, J., & Vişan, M. (2025). Determination of Schrödinger nonlinearities from the scattering map. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ada1bf
Killip, Rowan, Jason Murphy, and Monica Vişan. “Determination of Schrödinger Nonlinearities from the Scattering Map.” Nonlinearity. IOP Publishing, 2025. https://doi.org/10.1088/1361-6544/ada1bf.
R. Killip, J. Murphy, and M. Vişan, “Determination of Schrödinger nonlinearities from the scattering map,” Nonlinearity, vol. 38, no. 1. IOP Publishing, 2025.
Killip R, Murphy J, Vişan M. 2025. Determination of Schrödinger nonlinearities from the scattering map. Nonlinearity. 38(1), 015021.
Killip, Rowan, et al. “Determination of Schrödinger Nonlinearities from the Scattering Map.” Nonlinearity, vol. 38, no. 1, 015021, IOP Publishing, 2025, doi:10.1088/1361-6544/ada1bf.
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