University of Oulu

Valery Serov 2018 J. Phys.: Conf. Ser. 1141 012112

Fixed energy problem for nonlinear Schrödinger operator

Saved in:
Author: Serov, Valery1
Organizations: 1Professor of applied mathematics, University of Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Persistent link:
Language: English
Published: IOP Publishing, 2018
Publish Date: 2019-05-27


This work studies the inverse fixed energy scattering problem for the generalised nonlinear Schrödinger operators. We prove that in a three-dimensional case the unknown compactly supported generalised nonlinear potential (with some restriction for this potential) from \(L^{2}\) space can be uniquely determined by the scattering data with fixed positive energy (meaning that we have the knowledge of the scattering amplitude with fixed non-zero spectral parameter). The results are based on the new estimates for the Faddeev’s Green function in \(L^{∞}\). These results may have applications in nonlinear optics for the saturation model. In particular, the constant coefficients of this model can be uniquely reconstructed by the scattering data with fixed energy.

see all

Series: Journal of physics. Conference series
ISSN: 1742-6588
ISSN-E: 1742-6596
ISSN-L: 1742-6588
Volume: 1141
DOI: 10.1088/1742-6596/1141/1/012112
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This work was supported by the Academy of Finland (Finnish Programme for Centres of Excellence in Research, Inverse Modelling and Imaging, no. 312123, 2018-2025).
Academy of Finland Grant Number: 312123
Detailed Information: 312123 (Academy of Finland Funding decision)
Copyright information: Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.